hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Ran space
In mathematics, the Ran space (or Ran's space) of a topological space X is a topological space  whose underlying set is the set of all nonempty finite subsets of X: for a metric space X the topology is induced by the Hausdorff distance. The notion is named after Ziv Ran.

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.
The Center of the World
The Center of the World is a 2001 American drama film directed by Wayne Wang and shot on digital video. It stars Peter Sarsgaard as a dot-com millionaire who hires a drummer/stripper (Molly Parker) to stay with him in Las Vegas for three days for US$10,000. The film was screened out of competition at the 2001 Cannes Film Festival.

2001 Cannes Film Festival
The 54th Cannes Film Festival took place from 9 to 20 May 2001. Norwegian actress and director Liv Ullmann served as the Jury President of the main competition; she replaced American actress and filmmaker Jodie Foster, who had to step down due to scheduling conflicts with the film Panic Room. Italian filmmaker Nanni Moretti won the Palme d'Or for the drama film The Son's Room.

The festival opened with Moulin Rouge! by Baz Luhrmann, and closed with Savage Souls by Raúl Ruiz.
McFetridge
McFetridge is a surname, anglicized form of Scottish Gaelic Mac Pheadruis, patronymic from a Gaelic form of the given name Peter. Notable people with the surname include:

Duncan McFetridge (born 1952), Australian politician

Edward C. McFetridge (1836–1914), American lawyer, businessman and politician

Jack McFetridge (1869–1917), American baseball player

Olcan McFetridge (born 1963), Irish hurler

Peter McFetridge (born 1986), Canadian lacrosse player

William McFetridge (1893–1969), American labor leader

Olcan McFetridge
Olcan McFetridge (born 1963 in Armoy, County Antrim) is an Irish former sportsperson.  He played hurling with his local club Armoy and was a member of the Antrim senior inter-county team in the 1980s and 1990s.
St. Matthew Evangelical Lutheran School
St. Matthew Evangelical Lutheran School is a historic Lutheran school building located at 2101-2107 W. 21st Street in Chicago, Illinois. Built in 1882, it is one of the only surviving Italianate school buildings in Chicago. While the Italianate style was popular in Chicago in the second half of the 19th century, it was mainly used in homes and commercial buildings rather than institutional buildings, making the school's design uncommon even for its era. The school's distinctive Italianate features include its tall windows with arched lintels, its symmetrical front facade, its double bracketed cornice, and the cupola atop its roof. The school is also one of the oldest remaining school buildings in the Lower West Side and its adjacent community areas; only four older schools remain within these nine community areas, and St. Ignatius College Prep is the only older parochial school.

The building was added to the National Register of Historic Places on January 27, 2000.

Lower West Side, Chicago
Lower West Side is one of the 77 community areas of Chicago in Illinois, United States. It is three miles southwest of the Chicago Loop and its main neighborhood is Pilsen (/ˈpɪlsɪn/ PIL-sin). The Heart of Chicago is a neighborhood in the southwest corner of the Lower West Side.
Swift River
Swift River is the name of a Yukon town and several rivers:

Canada

Swift River (Cottonwood River), British Columbia

Swift River (Teslin Lake), British Columbia

Jamaica

Swift River (Jamaica)

New Zealand

Swift River, New Zealand

United Kingdom

River Swift, a tributary of the River Avon (Warwickshire)

United States

Swift River (Alaska)

Swift River (Bearcamp River), a tributary of the Bearcamp River, New Hampshire

Swift River (Maine), a tributary of the Androscoggin River

Swift River (Minnesota)

Swift River (Saco River), a tributary of the Saco River, New Hampshire

Swift River (Ware River), a tributary of the Ware River, Massachusetts

Swift River (Westfield River), a tributary of the Westfield River, Massachusetts

Swift River (Teslin Lake)
The Swift River is a river that begins in Yukon Territory and flows southwest into British Columbia to its mouth at the east side of Teslin Lake on the Teslin River system. The river drains the uppermost portion of the Cassiar Mountains and in its lower reaches traverses the Nisutlin Plateau, which lies along the east side of Teslin Lake north of the mouth of the Jennings River, which is to the south of the Swift.

The river is one of two in British Columbia known as the Swift, the other of the same name is a tributary to the Cariboo River in the eastern parts of the region of the same name.
Hillsborough station (North Carolina)
Hillsborough station is a planned infill train station in Hillsborough, North Carolina, located on the North Carolina Railroad (NCRR). According to town officials, the station building will have a meeting space, similar to Kannapolis station. When it is completed, Amtrak's Carolinian and Piedmont will serve the station. Along with the Durham station it will be the nearest Amtrak stations to the University of North Carolina at Chapel Hill.

North Carolina Railroad
The North Carolina Railroad (reporting mark NCRR) is a 317-mile (510 km) state-owned rail corridor extending from Morehead City, North Carolina, to Charlotte. The railroad carries over 70 freight trains (operated by the Norfolk Southern Railway) and ten passenger trains (Amtrak's Carolinian and Piedmont) daily. The railroad works with the North Carolina Department of Commerce and the North Carolina Department of Transportation on capital-improvement projects.
1930 Monza Grand Prix
The 1930 Monza Grand Prix was a Grand Prix motor race held at the Autodromo Nazionale di Monza on 7 September 1930. There were four 14-lap heats (separated by class), a 7-lap repêchage, and a 35-lap final, which was won by Achille Varzi in a Maserati. His teammates, Luigi Arcangeli and Ernesto Maserati, completed the podium.

Ernesto Maserati
Ernesto Maserati (4 August 1898 – 1 December 1975) was an Italian automotive engineer and racer, with Maserati of Modena since its inception in Bologna on 14 December 1914, together with his brothers Alfieri Maserati (leader), Ettore Maserati, Bindo Maserati and others.

Ernesto led the workshop during World War I, as his brothers joined the military. His racing career started in 1924, when he won the Italian drivers championship in 1927 in the Maserati Tipo 26, in 1930 using the Tipo 8C-2500.

After his brother Alfieri Maserati died in 1932, Ernesto became the director, chief engineer as well as sole racing car driver of the company. The company was sold to Adolfo Orsi in 1937, but the brothers remained on a ten-year contract, Ernesto participating in the design of the Maserati A6 after World War II.  He left with Ettore and Bindo (1947), to found the O.S.C.A. car company.

He died at Bologna in 1975.
Zygocarpum
Zygocarpum is a genus of flowering plants in the legume family, Fabaceae. It includes six species of shrubs and small trees native to Somalia and Socotra, and to Yemen and Oman on the southwestern Arabian Peninsula. Three species are endemic to Somalia, two to the Arabian Peninsula, and one to Socotra. Typical habitats include seasonally-dry tropical woodland, thicket, and bushland, often on limestone and less often on granite-derived or sandy soils, up to 2000 meters elevation.

The genus was recently assigned to the informal monophyletic Dalbergia clade of the Dalbergieae. A dichotomous key of the species of Zygocarpum has been published.

Socotra
Socotra, locally known as Saqatri, is a Yemeni island in the Indian Ocean. It is situated between the Gulf of Aden, the Guardafui Channel and the Arabian Sea, and lies near major shipping routes. The largest of the six islands in the Socotra archipelago, it comprises around 95% of the landmass of the archipelago. It lies 380 kilometres (205 nautical miles) south of the Arabian Peninsula and 232 km (125 nmi) east of the Horn of Africa. The inhabitants of the island are called Socotrans, and they speak Arabic and Soqotri.

Socotra is home to a high number of unique species that are endemic. Up to a third of its plant life is unique. Due to the island's unusual geography, it has been described as "the most alien-looking place on Earth". The island measures 132 km (82 mi) in length and 42 km (26 mi) across at its widest. In 2008, Socotra was recognised as a UNESCO World Heritage Site.
Valtesse de La Bigne
Émilie-Louise Delabigne, known as Countess Valtesse de La Bigne (1848, in Paris – 29 July 1910, in Ville-d'Avray), was an elite French courtesan and demi-mondaine  who rose through the social ranks to mix with Paris's most glamorous elite. Although born to a working-class family in Paris, she built a life for herself and became a muse to artists like Henri Gervex, Édouard Manet, as well as novelist Émile Zola. Beyond her career as a courtesan, she was also an actress, an art collector, and salonnière.

Demimonde
Demimonde is a French 19th-century term referring to women on the fringes of respectable society, and specifically to courtesans supported by wealthy lovers. The term is French for "half-world", and derives from an 1855 play called Le Demi-Monde, by Alexandre Dumas fils, dealing with the way that prostitution at that time threatened the institution of marriage. The demi-monde was the world occupied by elite men and the women who entertained them and whom they kept.
Never Give Up (1978 film)
Never Give Up (Japanese: 野性の証明, Hepburn: Yasei no shōmei) is a 1978 Japanese drama film, based on a novel by Seiichi Morimura. It was directed by Junya Sato and produced by Haruki Kadokawa. Toei Company released the film on October 7, 1978, in Japan.

Haruki Kadokawa
Haruki Kadokawa (角川 春樹, Kadokawa Haruki; born January 8, 1942, in Tokyo) is a Japanese entrepreneur and filmmaker. He is the son of Genyoshi Kadokawa, the founder of the publishing company Kadokawa Shoten. He took over as president of the company in 1975 after his father's death. He entered the film industry as a producer and introduced a technique called media mix, which involved mass promotion and talent scouting for new artists in publishing, film, and television. In 1993, he was arrested for drug smuggling. He resigned as president of Kadokawa Shoten, founding Kadokawa Haruki Corporation instead.
Menagerie
A menagerie is a collection of captive animals, frequently exotic, kept for display; or the place where such a collection is kept, a precursor to the modern zoo or zoological garden.

The term was first used in 17th-century France, referring to the management of household or domestic stock. Later, it came to be used primarily in reference to aristocratic or royal animal collections. The French-language Methodical Encyclopaedia of 1782 defines a menagerie as an "establishment of luxury and curiosity". Later on, the term referred also to travelling animal collections that exhibited wild animals at fairs across Europe and the Americas.

Vincennes
Vincennes (/vɪnˈsɛnz, væ̃ˈsɛn/; French: [vɛ̃sɛn] ⓘ) is a commune in the Val-de-Marne department in the eastern suburbs of Paris, France. It is located 6.7 km (4.2 mi) from the centre of Paris. Vincennes is famous for its castle: the Château de Vincennes. It is next to but does not include the Bois de Vincennes, from which it took its name, which is attached to the city of Paris.
Lucky Jim Camp
Lucky Jim Camp sometimes called Lucky Camp is a ghost town site in Clark County, Nevada.  It was within New Mexico Territory when founded in 1862.

It was a mining camp in El Dorado Canyon in the Colorado Mining District in the 1860s.  Its site lies on the north side of the canyon, south of the Techatticup Mine, at an elevation of 2,444 feet (745 m) and above the mouth of January Wash at its confluence with El Dorado Canyon.

New Mexico Territory
The Territory of New Mexico was an organized incorporated territory of the United States from September 9, 1850, until January 6, 1912. It was created from the U.S. provisional government of New Mexico, as a result of Nuevo México becoming part of the American frontier after the Treaty of Guadalupe Hidalgo. It existed with varying boundaries until the territory was admitted to the Union as the U.S. state of New Mexico in 1912. This jurisdiction was an organized, incorporated territory of the US for nearly 62 years, the longest period of any territory in the contiguous United States.
Samuel Woolley
Samuel Woolley is an American media studies scholar and expert on computational propaganda and misinformation. Woolley was a founder of the Computational Propaganda Research Project at the University of Oxford in 2013, and the Institute for the Future's Digital Intelligence Lab. As of 2025, he is an associate professor at the University of Pittsburgh in their Department of Communication, and holds the University's William S. Dietrich II Endowed Chair In Disinformation Studies.

Woolley's books include The Reality Game: How the Next Wave of Technology Will Break the Truth (2020) and Manufacturing Consensus: Understanding Propaganda in the Era of Automation and Anonymity (2023).

Media studies
Media studies is a discipline and field of study that deals with the content, history, and effects of various media; in particular, the mass media. Media studies may draw on traditions from both the social sciences and the humanities, but it mostly draws from its core disciplines of mass communication, communication, communication sciences, and communication studies.

Researchers may also develop and employ theories and methods from disciplines including cultural studies, rhetoric (including digital rhetoric), philosophy, literary theory, psychology, political science, political economy, economics, sociology, anthropology, social theory, art history and criticism, film theory, and information theory.
Maurice Barrow (puritan)
Maurice Barrow (1597/98–1666) was a puritan lawyer and committeeman active in Suffolk during the English Civil War. He was also noted for his exceeding wealth.

Maurice was the son of William Barrow of Westhorpe, Suffolk. and his second wife, Elizabeth Daundy. He attended St John's College, Cambridge matriculating in 1612. He practiced law at Gray's Inn.

He was High Sheriff of Suffolk twice, in 1628 and 1643.

Barrow married Mary Smythe, a daughter of Richard Smythe of Leeds Castle.

Political party committee
In the United States, a political party committee is an organization, officially affiliated with a political party and registered with the Federal Election Commission (FEC), which raises and spends money for political campaigning. Political party committees are distinct from political action committees, which are formally independent of political parties and subject to different rules.

Though their own internal rules differ, the two major political parties (Democrats and Republicans) have essentially parallel sets of committees; third parties have more varied organizational structures.
2026 Arizona elections
A general election will be held in the U.S. state of Arizona on November 3, 2026. Primary elections will take place on July 21, 2026. The state-wide races in Arizona as well as the House races are expected to get significant attention due to its status as a battleground state. Arizona used to be a solid red state but had drifted into being a purple state by the 2020s, with Democrats holding both Senate seats and the governorship, in addition to Democrat Joe Biden winning the state in the 2020 presidential election. However, Republican Donald Trump won by a 5 point margin in 2024, showing his strongest performance out of every battleground state in that election. This is the first election cycle since 2014 that Arizona will not have a U.S. Senate election.

Kevin Thompson (politician)
Kevin Thompson is an American politician and former enlisted member of the United States Air Force and current member of the Arizona Corporation Commission. A member of the Republican Party, Thompson served the citizens of Mesa, AZ as Councilmember of District 6 from January 2015 to January 2023 prior to being elected to the Commission in November 2022.
Undercover Law
Undercover Law (Spanish title: La ley secreta) is a Colombian drama television series produced by Caracol Televisión that premiered via streaming on 31 August 2018 on Netflix. It stars Viña Machado, Luna Baxter, Juana del Río, Valeria Galviz, Tommy Vásquez, Luis Mesa, Katherine Vélez, Variel Sánchez, Ricardo Vesga, and Juan Manuel Mendoza. The series is based on a group of women who form a special police force. The production of the series began on 30 October 2017 and it is available in 4K ultra-high-definition television.

It was released through Caracol Televisión from Colombia on 1 October 2019.

4K resolution
4K resolution is a horizontal display resolution of approximately 4,000 pixels. For digital cinematography, it is 3996 × 2160 (DCI 4K), typically with a 16.65:9 (1.85:1) aspect ratio; for digital television, it is 3840 × 2160 (4K UHD), typically with a 16:9 (1.78:1) aspect ratio.

The 4K television market share increased as prices fell dramatically throughout 2013 and 2014.
Ier
The Ier or Eriu (Hungarian: Ér) is a right tributary of the river Barcău (Berettyó) in Romania and Hungary. It discharges into the Barcău in Pocsaj. The Andrid Dam is constructed on this river. The Ier flows through the villages Mihăieni, Eriu-Sâncrai, Ghirolt, Rădulești, Hotoan, Sudurău, Dindești, Andrid, Sălacea, Cherechiu, Săcueni, Diosig in Romania, and Pocsaj in Hungary. In Romania, its length is 100 km (62 mi) and its basin size is 1,392 km2 (537 sq mi).

Sălacea
Sălacea (Hungarian: Szalacs) is a commune in Bihor County, Crișana, Romania with a population of 3,036. It is composed of two villages, Otomani (Ottomány) and Sălacea. The Otomani culture, a local Bronze Age culture (2100-1600 BC), takes its name from the village of Otomani.
Pouncey
Pouncey is a surname. Notable people with the surname include:

Maurkice Pouncey (born 1989), American football player

Mike Pouncey (born 1989), American football player, twin brother of Maurkice

Peter Pouncey (born 1937), British author, classicist, and university president

Maurkice Pouncey
LaShawn Maurkice Pouncey (born July 24, 1989) is an American former professional football player who was a center for 11 seasons with the Pittsburgh Steelers of the National Football League (NFL). He played college football for the Florida Gators, where he was a member of a BCS National Championship team, recognized as a consensus All-American, and won the 2009 Rimington Trophy, awarded annually to the best college football center. He was selected by the Steelers in the first round of the 2010 NFL draft. Pouncey was a nine-time Pro Bowler and named to five All-Pro teams, and was also named to the NFL 2010s All-Decade Team. He is the twin brother of former NFL center Mike Pouncey.
Aero East Europe Sila
The Aero East Europe Sila (English: force, power or strength and also short for Serbian industry light aircraft) is a family of Serbian ultralight and light aircraft, designed and produced by Aero East Europe of Kraljevo and later of Jagodina, introduced at the AERO Friedrichshafen show in 2013. The design is supplied complete and ready-to-fly.

Jagodina
Jagodina (Serbian Cyrillic: Јагодина, pronounced [jâɡodina] ⓘ) is a city and the administrative center of the Pomoravlje District in central Serbia. It is situated on the banks of the Belica River, in the geographical region of Šumadija. The city itself has a population of 34,892 inhabitants, while its administrative area comprises 64,644 inhabitants.
Petros Palian
Petros "Peter" Palian (Persian: پطروس پالیان, Armenian: Պետրոս Պալյան; 1 May 1931 – 15 March 2023) was an Iranian Armenian cinematographer and videographer. He was the videographer for Shah Mohammad Reza Pahlavi in the 1950s.

Videography
Videography involves capturing moving images on electronic media (such as: videotape, direct to disk recording, or solid state storage), and can include streaming media. It encompasses both video production and post-production methods. Historically videography was considered the video counterpart to cinematography, which involved recording moving images on film stock. However, with the advent of digital video recording in the late 20th century, the distinction between the two has become less clear as  both use similar intermediary mechanisms. Today, any video work can be referred to as videography, while commercial motion picture production is typically termed cinematography.

A videographer works in the field of videography and video production. News broadcasting heavily relies on live television, where videographers are involved in electronic news gathering (ENG) of local news stories.
Ringway
Ringway can mean:

Ringway, Greater Manchester, a civil parish within the city of Manchester, England
Manchester Airport, initially known as Ringway Airport, located near Ringway.
RAF Ringway, the name for Manchester Airport during the second world war

Ringway, Manchester
Ringway is a civil parish on the southern border of Manchester, England. Historically in Cheshire, it is the only civil parish in the city of Manchester. The population at the 2011 census was 103. Ringway is home to Manchester Airport.
Hetton-le-Hole
Hetton-le-Hole is a town in the civil parish of Hetton, in the Sunderland district, in the county of Tyne and Wear, England. Until 1974 it was in County Durham.

The A182 road runs through the town, between Houghton-le-Spring and Easington Lane which borders the County Durham District, off the A69t and east of the A1(M).

The parish includes the villages of Easington Lane and Warden Law, had a population of 14,402 in 2001. The parish also includes Hetton proper, along with East Rainton, Middle Rainton (West Rainton is a separate parish), Low Moorsley and High Moorsley.

Great Eppleton Wind Farm, a wind farm originally of four dual-bladed alternators, provides electricity to the National Grid. The original wind turbines have been replaced by larger three-bladed versions. The turbines are far enough away from local houses not to cause any audible disturbance.

County Durham (district)
County Durham is a unitary authority area in the ceremonial county of County Durham, England. It is governed by Durham County Council. The district has an area of 2,226 square kilometres (859 sq mi), and contains 135 civil parishes. It forms part of the larger ceremonial county of Durham, together with boroughs of Darlington, Hartlepool, and the part of Stockton-on-Tees north of the River Tees.