hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Discrete space
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open in the discrete topology so that in particular, every singleton subset is an open set in the discrete topology.

Subset
In mathematics, a set A is a subset of a set B if and only if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.

When quantified,  is represented as

One can prove the statement  by applying a proof technique known as the element argument:

Let sets A and B be given. To prove that 
suppose that a is a particular but arbitrarily chosen element of A
show that a is an element of B.

The validity of this technique can be seen as a consequence of universal generalization: the technique shows  for an arbitrarily chosen element c. Universal generalisation then implies  which is equivalent to  as stated above.
Apertura 2012 Copa MX
The Copa 2012 MX Apertura was the 68th staging of the Copa MX football tournament, the 41st staging in the professional era and the first played since the 1996–97 edition.

The tournament started on July 24, 2012, and concluded on October 31, 2012. In the final, Dorados de Sinaloa won the cup over Correcaminos 5–4 on penalties, after a 2–2 draw.

Celaya F.C.
Celaya Fútbol Club, simplified as Celaya FC, is a Mexican professional football club based in Celaya, Guanajuato. It competes in Liga Premier, the third level division of Mexican football, and plays its home matches at the Estadio Miguel Alemán Valdés. Founded in 1954, the club changed its name to Real Celaya in 1991, then as Atlético Celaya in 1994. After its dissolution in 2002, the club returns as Cajeteros de Celaya (2003–2007), and later renamed as Club Celaya in 2007. Since 2008, the club uses its original name.
Chace Crawford
Christopher Chace Crawford (born July 18, 1985) is an American actor. He is known for his television portrayals of Nate Archibald on the series Gossip Girl (2007–2012) and of Kevin Moskowitz / The Deep in the television series The Boys (2019–present) and the resulting franchise. He is also known for starring in the films The Covenant (2006), The Haunting of Molly Hartley (2008), Twelve (2011), and What to Expect When You're Expecting (2012).

Plano, Texas
Plano (/ˈpleɪnoʊ/ PLAY-noh; Spanish for 'flat surface') is a city in the U.S. state of Texas, where it is the largest city in Collin County. A small portion of Plano is located in Denton County. Plano is one of the principal suburbs of the Dallas–Fort Worth metroplex. With a population of 285,494 at the 2020 census, it is the ninth most-populous city in Texas, and, respectively, the 73rd most populous city in the United States.

Plano serves as an important hub of the economy of Dallas. It is home to the headquarters of Frito-Lay, JCPenney, Pizza Hut, and Toyota Motor North America.
Night Slave
Night Slave (ナイト・スレイブ) is an eroge run and gun video game  released in 1996 for the NEC PC-98 computer. The game's design and gameplay draws inspiration from the Assault Suits series, particularly Assault Suits Valken (1992), as well as the Gradius series.  It employs many action role-playing game elements such as permanently levelling up the mecha and various weapons using power-orbs obtained from defeating enemies as well as storyline cut scenes, which occasionally contain lesbian adult content. The game's armaments system also employs recoil physics, while the gameplay is varied, including environments such as rainy jungles, snowy wastes, and alien bases.

Eroge
An eroge (エロゲー, erogē, pronounced [eɾoɡe(ː)]), also called an H-game (エッチゲーム, ecchi game), is a Japanese genre of erotic video game. The term encompasses a wide variety of Japanese games containing erotic content across multiple genres. The first eroge were created in the 1980s, and many well-known companies in the Japanese gaming industry originally produced and distributed them. Some eroge are primarily focused on erotic content, while others, such as Key's Kanon, only contain occasional scenes in an otherwise non-erotic work. Games in the latter category are often re-released with sexual content removed for general audiences. Throughout its history, the genre has faced controversy for its use of explicit sexual content, and as a result has been banned from several console platforms.
Westgate, Canterbury
The Westgate is a medieval gatehouse in Canterbury, Kent, England. This 60-foot (18 m) high western gate of the city wall is the largest surviving city gate in England. Built of Kentish ragstone around 1379, it is the last survivor of Canterbury's seven medieval gates, still well-preserved and one of the city's most distinctive landmarks. The road still passes between its drum towers. This scheduled monument and Grade I listed building houses the West Gate Towers Museum as well as a series of historically themed escape rooms.

Gatehouse
A gatehouse is a type of fortified gateway, an entry control point building, enclosing or accompanying a gateway for a town, religious house, castle, manor house, or other fortification building of importance. Gatehouses are typically the most heavily armed section of a fortification, to compensate for being structurally the weakest and the most probable attack point by an enemy. There are numerous surviving examples in France, Austria, Germany, England and Japan.
Urman-Bishkadak
Urman-Bishkadak (Russian: Урман-Бишкадак; Bashkir: Урман-Бишҡаҙаҡ, Urman-Bişqaźaq) is a rural locality (a selo) and the administrative centre of Urman-Bishkadaksky Selsoviet, Ishimbaysky District, Bashkortostan, Russia. The population was 613 in 2010. There are seven streets. It is eleven kilometres north of Ishimbay (the district's administrative centre) by road. Yar-Bishkadak is the nearest rural locality.

Yar-Bishkadak
Yar-Bishkadak (Russian: Яр-Бишкадак; Bashkir: Яр-Бишҡаҙаҡ, Yar-Bişqaźaq) is a rural locality (a village) in Urman-Bishkadaksky Selsoviet, Ishimbaysky District, Bashkortostan, Russia. The population was 539 as of 2010. There are 5 streets in this locality.
Terraserver.com
TerraServer was a commercial website specializing in aerial and satellite imagery which was originally launched in 1997.  It is owned and operated by TerraServer.com, Inc. in Raleigh, North Carolina.  The company was previously named Aerial Images until May 2002 when the assets of Aerial Images were sold and the company renamed itself TerraServer.com, Inc.

Satellite imagery
Satellite images (also Earth observation imagery, spaceborne photography, or simply satellite photo) are images of Earth collected by imaging satellites operated by governments and businesses around the world. Satellite imaging companies sell images by licensing them to governments and businesses such as Apple Maps and Google Maps.
Z-TER (Z 21500)
The Z-TER (Z 21500) is a French model of electric multiple unit regional passenger train, manufactured by Alstom and Bombardier Transportation, and operated by SNCF.

They are used on regional links, and can be coupled with another Z-TER. They are derived from the French diesel passenger regional train "X-TER" (X 72500), and is the first regional train to reach 200 km/h.

Their main characteristic is their ability to travel at 124.27 mph, which constitutes a first for TER self-propelled equipment. This ability, used every day over several sections of conventional lines, is also operated for the first time on a high speed line since 2017. This is a first in France, thanks to an adaptation of eight of these elements to signaling specific to LGVs, then renumbered as Z 21700.

As other regional trains, they are owned by the French regions, and are dispatched as :

19 "Pays de la Loire" region

15 "Centre" region

6 "Aquitaine" region

17 "Bretagne" region

Transport express régional
Transport express régional (French pronunciation: [tʁɑ̃spɔʁ ɛksprɛs ʁeʒjɔnal], usually shortened to TER) is the brand name used by the SNCF, the French national railway company, to denote rail service run by the regional councils of France, specifically their organised transport authorities. The network serves French regions; Île-de-France (Transilien) and Corsica (CFC) have their own specific transport systems. Every day, over 800,000 passengers are carried on 5,700 TER-branded trains.

TER is part of SNCF Voyageurs, a branch of the SNCF dealing with urban and regional passenger rail, which also includes Transilien, Intercités, Chemins de fer de la Corse (CFC), Keolis, and Effia.
Passiontide
Passiontide (in the Christian liturgical year) is a name for the last two weeks of Lent, beginning on the Fifth Sunday of Lent, long celebrated as Passion Sunday, and continuing through Lazarus Saturday. It commemorates the suffering of Christ (Latin passio = “suffering”). The second week of Passiontide is Holy Week, ending on Holy Saturday.

Holy Saturday
Holy Saturday (Latin: Sabbatum Sanctum), also known as Great and Holy Saturday, Low Saturday, the Great Sabbath, Hallelujah Saturday, Saturday of the Glory, Easter Eve, Joyous Saturday, the Saturday of Light, Good Saturday, or Black Saturday, among other names, is the final day of Holy Week, between Good Friday and Easter Sunday, and when Christians prepare for the Christian feast of Easter.

The day commemorates the Harrowing of Hell while Jesus Christ's body lay in the tomb. Christians of the Catholic, Lutheran, and Anglican denominations begin the celebration of the Easter Vigil service on Holy Saturday, which provides a transition to the season of Eastertide; in the Moravian Christian tradition, graves are decorated with flowers during the day of Holy Saturday and the celebration of the sunrise service starts before dawn on Easter Sunday. Congregations of the Reformed and Methodist denominations may hold either the Easter Vigil or an Easter Sunday sunrise service.
Honda PC50
The Honda PC50 is a moped produced by the Honda Motor Company in Japan from May 1969 until at least 1983. The PC50, though much smaller and lighter, had some similar features to Honda's popular C50 /70 /90 Super Cub line, with a step-through pressed-steel frame, a fuel tank under the saddle, a chain cover, and optionally equipped with  leg shields,

Honda Super Cub
The Honda Super Cub (or Honda Cub) is an underbone motorcycle manufactured and marketed by Honda, featuring a four-stroke single-cylinder engine ranging in displacement from 49 to 124 cc (3.0 to 7.6 cu in).

In continuous manufacture since 1958 with production surpassing 60 million in 2008, 87 million in 2014, and 100 million in 2017, the Super Cub is the most produced motor vehicle* in history. Variants include the C50, C65, C70 (including the Passport), C90, C100 (including the EX) and it used essentially the same engine as the Sports Cub C110, C111, C114 and C115 and the Honda Trail series.

The Super Cub's US advertising campaign, You meet the nicest people on a Honda, had a lasting impact on Honda's image and on American attitudes to motorcycling, and is often used as a marketing case study.
Development Bureau
The Development Bureau (DEVB; Chinese: 發展局) is a policy bureau of the Government of Hong Kong responsible for urban planning and renewal, land administration, infrastructure development, building safety, landscape, greening & tree development, water supplies, flood prevention and heritage conservation.

The Bureau is supervised by the Secretary for Development.

Secretary for Development
The Secretary for Development of the Hong Kong Government is responsible for planning, land development and public works related development policy in Hong Kong.  The position was created in 2007 to replace portions of the previous portfolios of Secretary for the Environment, Transport and Works and Secretary for Housing, Planning and Lands.
Spirit FM (Narrandera)
Spirit FM is a community radio station broadcasting to the town of Narrandera, Australia, which first aired in 2005. Programs are broadcast from a studio in the Narrandera railway station, and relayed to an FM transmitter on top of the water reservoir at the corner of Gordon Street and Broad Street.

Narrandera
Narrandera (/nəˈrændərə/ nə-RAN-dər-ə; wiradjuri: Narrangdhuray), until around 1949 also spelled "Narandera", is a town located in the central Riverina region of south-western New South Wales, Australia. The town lies on the junction of the Newell and Sturt highways, adjacent to the Murrumbidgee River, and it is considered the gateway to the Murrumbidgee Irrigation Area. At the 2021 census, Narrandera had a population of 3,783.
Begum Khaleda Zia Mahabiddalay
Begum Khaleda Zia Mahabiddalay is an educational institution located at Kalaroa Upazila in the Satkhira district of Bangladesh which was established in 2000. The college imparts education at higher secondary, and undergraduate levels under the Board of Intermediate and Secondary Education, Jashore, and National University. It is named after former prime minister Begum Khaleda Zia.

Satkhira District
Satkhira District (Bengali: সাতক্ষীরা জেলা; lit. 'Seven cucumbers') is a district in southwestern Bangladesh and is part of Khulna Division. It lies along the border with West Bengal, India. It is on the bank of the Arpangachhia River. The largest city and headquarters of this district is Satkhira.
Rattray Head
Rattray Head (listenⓘ), historically Rattray Point, is a headland in Buchan, Aberdeenshire, on the north-east coast Scotland. To north lies Strathbeg Bay and Rattray Bay is to its south. The dunes at Rattray Head beach can be up to 75 feet (23 m) high and stretch 17 miles (27 km) from St Combs to Peterhead.

Buchan
Buchan /ˈbʌxən/ is a coastal district in the north-east of Scotland, bounded by the Ythan and Deveron rivers. It was one of the original provinces of the Kingdom of Alba. It is now one of the six committee areas of Aberdeenshire.
Ålholm station
Ålholm station is a commuter rail railway station serving the northwestern part of the district of Valby in Copenhagen, Denmark. It is located on the Ring Line of Copenhagen's S-train network. The station opened on 8 January 2005 where Roskildevej crosses the railway line.

Rail transport in Denmark
The rail transport system in Denmark consists of 2,633 km (1,636 mi) of railway lines, of which the Copenhagen S-train network, the main line Helsingør-Copenhagen-Padborg (at the German border), and the Lunderskov-Esbjerg line are electrified. Most traffic is passenger trains, although there is considerable transit goods traffic between Sweden and Germany.

Maintenance work on most Danish railway lines is done by Banedanmark, a state-owned company that also allocates tracks for train operators. The majority of passenger trains are operated by DSB, with Arriva and Nordjyske Jernbaner and Midtjyske Jernbaner operating on some lines in Jutland. Goods transport is mainly performed by DB Schenker Rail, although other operators take care of a significant portion of the non-transit traffic.

Denmark is a member of the International Union of Railways (UIC). The UIC Country Code for Denmark is 86.
Indonesia International Motor Show
The Indonesia International Motor Show (formerly Gaikindo Auto Expo) is an annual automotive exhibition in Jakarta, Indonesia. It is organized by Dyandra Promosindo, a subsidiary of Kompas Gramedia. Since 2009, the exhibition is held at Jakarta International Expo Kemayoran in Pademangan, North Jakarta.

From 1986 to 2011, the exhibition started in July. From 2012 to 2015, the exhibition started in August or September. From 2016 to 2022, the exhibition started in April to May. Since 2023, the exhibition has started in February.

Kompas Gramedia Group
Kompas Gramedia is a major Indonesian media company.  It engages in several businesses, predominantly mass media, as well as hospitality, manufacturing, and event organizing.

The company's businesses consist of multiple divisions, such as media assets (including the Kompas daily newspaper; the Kompas TV television network; the Sonora radio network; the Gramedia bookstore chain, the Santika Indonesia hospitality chain, Dyandra event organization firm, and Graha Bumi Hijau, a tissue paper manufacturer known for its flagship brand, Tessa.
KDE Display Manager
KDE Display Manager (KDM) was a display manager (a graphical login program) developed by KDE for the windowing systems X11.

KDE Display Manager was based on the source code of X display manager and was the default display manager of the KDE Software Compilation, until it was retired in KDE Plasma 5 in favour of SDDM.

KDM allowed the user to choose a desktop environment or window manager at login. KDM used the Qt application framework. It is configurable via KDE's System Settings; its appearance can be customized by the user.

The default KDM login screen had a list of users. Each entry was comprised in the user's username, personal name (if available), and an icon. Next to the list is a greeting and a picture. One of the customization options is to replace the picture with an analog clock. From this screen the user can also run a user management tool, shut down or reboot the computer, or restart the X Window System.

KDE Software Compilation
The KDE Software Compilation (KDE SC) was an umbrella term for the desktop environment plus a range of included applications produced by KDE. From its 1.0 release in July 1998 until the release of version 4.4 in February 2010, the Software Compilation was simply known as KDE, which stood for K Desktop Environment until the rebrand. The then called KDE SC was used from 4.4 onward until the final release 4.14 in July 2014. It consisted of the KDE Plasma 4 desktop and those KDE applications, whose development teams chose to follow the Software Compilation's release schedule. After that, the KDE SC was split into three separate product entities: KDE Plasma, KDE Frameworks and KDE Applications, each with their own independent release schedules.
Imogene Peak
Imogene Peak, at 10,125 feet (3,086 m) above sea level is a peak in the Sawtooth Range of Idaho. The peak is located in the Sawtooth Wilderness of Sawtooth National Recreation Area in Custer County. The peak is located 1.83 mi (2.95 km) north of Parks Peak, its line parent. Farley Lake is located south of the peak, and Imogene Lake is west of the peak.

Sawtooth Range (Idaho)
The Sawtooth Range is a mountain range of the Rocky Mountains in central Idaho, United States, reaching a maximum elevation of 10,751 feet (3,277 m) at the summit of Thompson Peak. It encompasses an area of 678 square miles (1,756 km2) spanning parts of Custer, Boise, Blaine, and Elmore counties, and is bordered to the east by the Sawtooth Valley. Much of the mountain range is within the Sawtooth Wilderness, part of the Sawtooth National Recreation Area and Sawtooth National Forest.

The mountains were named for their jagged peaks.
1996 Fed Cup Americas Zone Group I – Pool A
Group A of the 1996 Fed Cup Americas Zone Group I was one of two pools in the Americas Zone Group I of the 1996 Fed Cup. Four teams competed in a round robin competition, with the top two teams advancing to the knockout stage.

1996 Fed Cup Americas Zone Group I – Knockout Stage
The Knockout Stage of the 1996 Fed Cup Americas Zone Group I was the final stage of the Zonal Competition involving teams from the Americas. Those that qualified for this stage placed first and second in their respective pools.

The four teams were then randomly drawn into a two-stage knockout tournament, with the winner advancing to the World Group II Play-offs.
Riolunato
Riolunato (Riolunatese: Ardodlà) is a comune (municipality) in the Province of Modena in the Italian region Emilia-Romagna, located about 60 kilometres (37 mi) southwest of Bologna and about 50 kilometres (31 mi) southwest of Modena. It is overlooked from the south by the Monte Cimone. Its fraction Le Polle, about 1,300 metres (4,300 ft) high, is one of the most important stations in the Monte Cimone Ski resort.

Riolunato borders the following municipalities: Fiumalbo, Frassinoro, Lama Mocogno, Montecreto, Palagano, Pievepelago, Sestola.

Pievepelago
Pievepelago (Frignanese: La Piéva or Piêvpèlegh) is a comune (municipality) in the Province of Modena in the Italian region of Emilia-Romagna in the heart of the northern Apennine Mountains. Situated on the Scoltenna River, in a mountain valley, it is a tourist resort crossed by the Via Vandelli.

It is about 70 kilometres (43 mi) southwest of Bologna, about 60 kilometres (37 mi) southwest of Modena, about 60 kilometres (37 mi) north of Lucca and about 70 kilometres (43 mi) northwest of Florence. It has a population of about 2200 inhabitants, spread among the main town and its frazioni, Sant'Annapelago, Roccapelago, Sant'Andreapelago and Tagliole.
NGC 1947
NGC 1947 is a peculiar lenticular galaxy in the constellation Dorado. The galaxy lies about 50 million light years away from Earth, which means, given its apparent dimensions, that NGC 1947 is approximately 75,000 light years across. It was discovered by James Dunlop on November 5, 1826.

Lenticular galaxy
A lenticular galaxy (denoted S0) is a type of galaxy intermediate between an elliptical (denoted E) and a spiral galaxy in galaxy morphological classification schemes. It contains a large-scale disc but does not have large-scale spiral arms.  Lenticular galaxies are disc galaxies that have used up or lost most of their interstellar matter and therefore have very little ongoing star formation. They may, however, retain significant dust in their disks. As a result, they consist mainly of aging stars (like elliptical galaxies).  Despite the morphological differences, lenticular and elliptical galaxies share common properties like spectral features and scaling relations. Both can be considered early-type galaxies that are passively evolving, at least in the local part of the Universe.  Connecting the E galaxies with the S0 galaxies are the ES galaxies with intermediate-scale discs.
Maliri people
The Maliri were a people, recalled by various communities in Kenya and Uganda today, that inhabited regions on the north east of and north west borders of Uganda and Kenya respectively and later spread to regions in southern Ethiopia.

Turkana people
The Turkana are a Nilotic people native to the Turkana County in northwest Kenya, a semi-arid climate region bordering Lake Turkana in the east, Pokot, Rendille and Samburu people to the south, Uganda to the west, South Sudan to the north-west (Didinga and Toposa) and Ethiopia to the north.
Peter Kennaugh
Peter Robert Kennaugh MBE (born 15 June 1989) is a Manx former professional racing cyclist, who rode professionally between 2010 and 2019 for Team Sky and Bora–Hansgrohe. In 2012 he won the gold medal as part of the Great Britain Team Pursuit team at the 2012 Summer Olympics, becoming the first Manxman in 100 years to win gold. On 5 April 2019, he announced that he was taking an indefinite break from professional cycling to focus on his mental health.

British Cycling National Track Championships
The British National Track Championships are a Track cycling event held annually and organised by the national governing body for track cycling (and other forms of cycling) in Great Britain, British Cycling (formerly the British Cycling Federation). The main events are various track cycling disciplines for elite athletes to determine the British national champions. However, competitions are also held in age-grade and disability/para-cycling categories. Winners receive a national champions jersey consisting of a white jersey with blue and red bands, which they are entitled to wear any time the contest the same event during that year.