hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation. This should not be confused with closed manifold.

Sets that are both open and closed are called clopen sets.

Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M.

Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g.  is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it (see further examples below). It is always possible to "fill all the holes", leading to the completion of a given space, as explained below.
USC Trojans baseball
The USC Trojans baseball program represents the University of Southern California in college baseball. Established in 1888, the team is a member of the National Collegiate Athletic Association and the Big Ten Conference.  USC’s home field is Dedeaux Field, which is named in honor of former head coach and National College Baseball Hall of Fame inductee Rod Dedeaux.

The USC Trojans are the most successful team in the history of American college baseball, having won more baseball national championships than any other program across all divisions of college baseball, with 12 national championships.

USC's most notable baseball coach was Rod Dedeaux, who coached from 1942 to 1986 and led the school to 11 of its NCAA championships, including five straight from 1970 to 1974.  The first Trojan national championship came in 1948.  The 12th and most recent NCAA championship came in 1998.

Jeff Clement
Jeffrey Burton Clement (born August 21, 1983) is an American former professional baseball player. Clement was a catcher and first baseman. He played in Major League Baseball (MLB) for the Seattle Mariners and Pittsburgh Pirates.

Clement attended the University of Southern California (USC), where he played college baseball for the USC Trojans and won the Johnny Bench Award as the nation's top collegiate catcher. The Mariners selected Clement in the first round (third overall) in the 2005 MLB draft. He struggled with injuries, which have limited his playing career.
Genesee, Wisconsin
Genesee is a town in Waukesha County, Wisconsin, United States. The population was 7,171 at the 2020 census. The unincorporated communities of Bethesda, Genesee, Genesee Depot, and Saylesville are in the town.

Waukesha County, Wisconsin
Waukesha County (/ˈwɔːkɪʃɔː/ ⓘ) is a county in the U.S. state of Wisconsin. As of the 2020 United States Census, the population was 406,978, making it the third-most populous county in Wisconsin. Its median income of $88,985 placed it as the only county in Wisconsin on the list of the 100 highest-income counties in the U.S. by median income as of 2020. Its county seat and largest city is Waukesha.

Waukesha County is included in the Milwaukee metropolitan area, and is one of the three WOW counties.
A13 motorway (Switzerland)
The A13 is a motorway, at times an Autostrasse (expressway), which runs from St. Margrethen in northeastern Switzerland through to Ascona in southern Switzerland, crossing the main chain of the Alps in the Grisons area. It is the southern half of European route E43.

Chur
Chur is the capital and largest town of the Swiss canton of the Grisons and lies in the Grisonian Rhine Valley, where the Rhine turns towards the north, in the northern part of the canton. The city, on the right bank of the Rhine, is reputedly the oldest town in Switzerland.

The official language of Chur is German, but the main spoken language is the local variant of Alemannic, known as Grisonian German. Romansh and Italian are significantly spoken in the city as a result of the trilingual identity of the canton.

On 1 January 2020 the former municipality of Maladers merged into Chur and on 1 January 2021 Haldenstein also merged. On 1 January 2025 the former municipality of Tschiertschen-Praden merged into Chur.
La Croix-sur-Gartempe
La Croix-sur-Gartempe (French pronunciation: [la kʁwa syʁ ɡaʁtɑ̃p], literally La Croix on Gartempe; Occitan: La Crotz) is a commune in the Haute-Vienne department in the Nouvelle-Aquitaine region in western France.

Haute-Vienne
Haute-Vienne (French: [ot vjɛn]; Occitan: Nauta Vinhana or Nauta Viena), also translated as Upper Vienne, is a department in the Nouvelle-Aquitaine region in southwest-central France. Named after the Vienne River, it is one of the twelve départements that together constitute Nouvelle-Aquitaine. The prefecture and largest city in the department is Limoges, the other towns in the department each having fewer than twenty thousand inhabitants. Haute-Vienne had a population of 372,359 in 2019.
Physics education
Physics education or physics teaching refers to the education methods currently used to teach physics. The occupation is called physics educator or physics teacher. Physics education research refers to an area of pedagogical research that seeks to improve those methods. Historically, physics has been taught at the high school and college level primarily by the lecture method together with laboratory exercises aimed at verifying concepts taught in the lectures. These concepts are better understood when lectures are accompanied with demonstration, hand-on experiments, and questions that require students to ponder what will happen in an experiment and why. Students who participate in active learning for example with hands-on experiments learn through self-discovery. By trial and error they learn to change their preconceptions about phenomena in physics and discover the underlying concepts. Physics education is part of the broader area of science education.

Science education
Science education is the teaching and learning of science to school children, college students, or adults within the general public. The field of science education includes work in science content, science process (the scientific method), some social science, and some teaching pedagogy. The standards for science education provide expectations for the development of understanding for students through the entire course of their K-12 education and beyond. The traditional subjects included in the standards are physical, life, earth, space, and human sciences.
Christian I, Prince of Anhalt-Bernburg
Christian I, Prince of Anhalt-Bernburg, also known as Christian of Anhalt, (11 May 1568 – 17 April 1630) was a German prince of the House of Ascania. He was ruling prince of Anhalt and, from 1603, ruling prince of the revived principality of Anhalt-Bernburg. From 1595 he was governor of Upper Palatinate, and soon became the advisor-in-chief of Frederick IV, Elector Palatine.

Anhalt-Bernburg
Anhalt-Bernburg was a principality  of the Holy Roman Empire and a duchy of the German Confederation ruled by the House of Ascania with its residence at Bernburg in present-day Saxony-Anhalt. It emerged as a subdivision from the Principality of Anhalt from 1252 until 1468, when it fell to the Ascanian principality of Anhalt-Dessau. Recreated in 1603, Anhalt-Bernburg finally merged into the re-unified Duchy of Anhalt upon the extinction of the line in 1863.
Fire on the Mountain (Bisson novel)
Fire on the Mountain is a 1988 novel by the American author Terry Bisson. It is an alternate history describing the world as it would have been had John Brown succeeded in his raid on Harper's Ferry and touched off a slave rebellion in 1859, as he intended.

Terry Bisson
Terry Ballantine Bisson (February 12, 1942 – January 10, 2024) was an American science fiction and fantasy author. He was best known for his short stories, including "Bears Discover Fire", which won the Hugo Award and the Nebula Award, and "They're Made Out of Meat".
Chandrapur Super Thermal Power Station
Chandrapur Super Thermal Power Station (often abbreviated as CSTPS) is a thermal power plant located in Chandrapur district in the Indian state of Maharashtra. The power plant is one of the coal based power plants of MAHAGENCO. The coal for the power plant is sourced from Durgapur and Padmapur Collieries of Western Coalfields Limited. The plant was officially inaugurated by the Prime Minister Indira Gandhi on 8 October 1984.

With the total capacity of 3340 MW, the plant is the largest power plant in the Maharashtra. It accounts for more than 25% of Maharashtra's total needs. The plant gets water supply from Erai Dam when in normal conditions. In the summer of 2010 due to less water in Erai, the plant also got water supply from Chargaon Dam.

Maharashtra State Power Generation Company
The Mahanirmiti or Mahagenco (Maharashtra State Power Generation plants Limited - MSPGCL) formerly known as MSEB (Maharashtra State Electricity Board) is a major power generating plants in the state of Maharashtra, India and a wholly owned subsidiary of Maharashtra State Electricity Board. With a total generation of 14,400 MW, it is the largest power producing plants in India controlled by state government. The power generated by Mahagenco is supplied to Maharashtra. It was a part of Maharashtra State Electricity Board until 6 June 2005.

It has been incorporated under Indian Companies Act 1956 pursuant to decision of government of Maharashtra to reorganise erstwhile history of Maharashtra State Electricity Board. Mahagenco has been incorporated in June 2005.
Brett Simpson
Brett Simpson is an American surfer and coach from Huntington Beach, California.  He is the inaugural head coach of the United States Olympic surfing team.  As a surfer, he won the 2009 U.S. Open of Surfing contest, and repeated again in 2010 by successfully defending his title against South African surfer Jordy Smith.   Simpson was named the Orange County Surfer of the Year in 2008 and 2009.

He is the son of American football player Bill Simpson.  He is a graduate of Huntington Beach High School.

US Open of Surfing
The U.S. Open of Surfing is a week-long surfing competition held annually during the summer in Huntington Beach, California. Generally held on the south side of the Huntington Beach Pier, the U.S. Open is part of the qualification process for the World Surf League and is a WSL QS 10,000 event. It is the largest surfing competition in the world. It has been owned by IMG since 2000.

As part of the event, notable people in the world of surfing are added to the Surfing Walk of Fame and to the Surfers' Hall of Fame, both directly across from the pier.
The Five-Storied Pagoda
The Five-Storied Pagoda (Gojūnotō, 五重塔) is a novella by writer Kōda Rohan. “It was originally written as a serialized piece of fiction in the intellectual newspaper Kokkai (Diet, or Parliament), beginning in November 1891 and ending in March of the following year. As  a consequence, chapter divisions in this story […] do not necessarily coincide with the breaks in plot progression or narrative pauses.”(15). The pagoda in the story is based on a pagoda donated to Tokyo by Tennō-ji.

Kōda Rohan
Kōda Shigeyuki (幸田 成行; 23 July 1867 – 30 July 1947), pen name Kōda Rohan (幸田 露伴; Japanese pronunciation: [koː.da (|) ɾoꜜ.haɴ]), was a Japanese author. His daughter, Aya Kōda, was also a noted author who often wrote about him.

Kōda wrote "The Icon of Liberty", also known as "The Buddha of Art" or "The Elegant Buddha", in 1889. A house in which Kōda lived, Kagyū-an (蝸牛庵; snail cottage), was rebuilt in 1972 by the Meiji Mura museum. Kōda was one of the first persons to be awarded the Order of Culture when it was established in 1937.
Danny Mitchell (EastEnders)
Danny Mitchell is a fictional character from the BBC soap opera EastEnders, played by soap newcomer Liam Bergin, who appeared from 21 January 2010 to 18 June 2010. He, along with his mother Glenda Mitchell (Glynis Barber), made a previously unannounced return on 30 December 2016, before departing again on 20 January 2017.

Liam Bergin
Liam Bergin (born 24 November 1985) is a British actor of Irish and Trinidadian descent. He trained at the Guildhall School of Music and Drama, graduating in 2008. He is currently best known for playing Danny Mitchell in EastEnders and Rupert in Trinity. He has also had minor roles in Doctors and the 2009 remake of Minder.

On 26 December 2009 it was announced he had been cast in the role of Danny Mitchell in the long-running soap opera EastEnders. The character was phased out by mutual consent from the show with executive producer Bryan Kirkwood in April 2010. He returned for a guest stint between December 2016 and January 2017.

Since the summer of 2014, he has been running an independent clothing brand called 'Boom Done Shop'.
Utica, Texas
Utica is a ghost town in Smith County, located in the U.S. state of Texas.

A postal office opened in 1890, when the population was still estimated 100 people. It was closed only 15 years later in 1905.

Smith County, Texas
Smith County is a county in the U.S. state of Texas. As of the 2020 census, its population was 233,479. Its county seat is Tyler. Smith County is named for James Smith, a general during the Texas Revolution. Smith County is part of the Tyler metropolitan statistical area and the Tyler–Jacksonville combined statistical area.
Volunteer grant
Volunteer grants are charitable gifts given to non-profit organizations by corporations in recognition of volunteer work being done by a company's employees. This practice is widespread in the United States.

Corporate giving programs created to encourage volunteerism by a corporation's employees by providing volunteer grants are called volunteer grant programs or Dollars for Doers programs.

Volunteering
Volunteering is an optional and freely chosen act of an individual or group giving their time and labor, often for community service. Many volunteers have specialized training in the fields that they work in, such as medicine, education, or emergency rescue. Others provide their services as needed, such as in response to a natural disaster.
Charles H. Heyl
Charles Heath Heyl (July 22, 1849 – October 12, 1926) was a US Army officer who received the Medal of Honor for his actions during the Indian Wars. He was born in Philadelphia.

Heyl was commissioned in the 23 Infantry Regiment in October 1873, and served as regimental adjutant from 1890 to 1891. During the Spanish–American War, he was promoted to major and assistant adjutant general in May 1898, and became an inspector general of volunteers in July. He was again promoted to lieutenant colonel in December 1899, and to colonel in July 1902. He retired in November 1904.

He was a member of the Sons of the American Revolution and the Order of the Indian Wars of the United States.

Heyl was buried in Arlington National Cemetery.

Order of the Indian Wars of the United States
The Order of the Indian Wars of the United States (OIWUS) is a military society founded in 1896 by officers of the United States Army who served in campaigns against Native Americans from the American Revolution to the late 19th century.
Folksingers 'Round Harvard Square
Folksingers 'Round Harvard Square is a collaborative folk album featuring Joan Baez, Bill Wood and Ted Alevizos; it is also Baez's debut appearance as six of the eighteen tracks were solos by her. The album was recorded by Stephen Fassett in "a friend's basement studio" in Boston, May 1959.

In 1963, an unauthorized reissue of the album was released on Squire Records as The Best of Joan Baez (minus four tracks that did not contain Baez' vocals — "Le Cheval dans la baignoire," "The Bold Soldier," "Lass from the Low Country" and "Rejected Lover"), but was withdrawn after Baez took legal action against it (by which time the album had already made the top-fifty on the U.S. albums charts).

Harvard Square is a place in Cambridge, Massachusetts; Baez had a residence at Club 47, located on the square.

William Barry Wood III
William Barry Wood III (19 February 1938 – 9 May 2024) was an American molecular and developmental biologist who served as a professor at the University of Colorado Boulder. His research focused on the genetic and molecular mechanisms of axis formation and patterning during early development, and he made influential contributions to the emerging field of molecular developmental biology. Wood was elected to the National Academy of Sciences at a notably young age (age 34) and received the NAS Award in Molecular Biology in recognition of his scientific achievements.

While a graduate student, Wood was also active in the Cambridge, Massachusetts folk music scene and appeared as "Bill Wood" on the 1960 album Folksingers 'Round Harvard Square, which featured early performances by Joan Baez. Wood's two sons, Oliver and Chris Wood, are professional musicians who perform as the roots-rock band The Wood Brothers.
Damian Dame (album)
Damian Dame is the only studio album by American R&B group Damian Dame, released May 14, 1991 via LaFace Records. The album did not chart on the Billboard 200, but it peaked at #21 on the Billboard R&B chart. Both members of Damian Dame died before a second album could be recorded.

Three singles were released from Damian Dame: "Exclusivity", "Right Down to It" and "Gotta Learn the Rhythm". "Exclusivity" was the most successful single from the album, peaking at #42 on the Billboard Hot 100 in 1991 and hitting #1 for 2 weeks on the Billboard R&B Charts in July 1991.

Damian Dame
Damian Dame was an American R&B group that was active in the early 1990s. It consisted of Bruce Edward "Damian" Broadus (September 13, 1966 – June 27, 1996) and Debra Jean "Deah Dame" Hurd (September 20, 1958 – June 27, 1994).
Being Brave
Being Brave is the first studio album by American singer-songwriter Amanda Shires. The album was recorded at Route 1, Acuff Studios in Acuff, Texas and co-produced by Shires and Andy Wilkinson. The album consists of several traditional and self-penned fiddle tunes. In May 2014, Shires told interviewer Alan Harrison of The Rocking Magpie that Being Brave "isn’t really a ‘debut’ album, but more of a showcase for my playing and occasional singing".

Amanda Shires
Amanda Rose Shires (born March 5, 1982) is an American singer-songwriter and fiddle player. Shires has released nine solo albums starting in 2005, her most recent being Nobody's Girl in 2025. In 2019, she founded a country music supergroup called The Highwomen alongside Brandi Carlile, Maren Morris and Natalie Hemby and has also performed as a member of the Texas Playboys, Thrift Store Cowboys, and Jason Isbell & the 400 Unit, as well as in a duo with Rod Picott. Along with Jason Isbell & the 400 Unit, Shires won the Grammy Award for Best Americana Album for their 2017 album The Nashville Sound.
Heritage Museums and Gardens
Heritage Museums and Gardens (100 acres), formerly the Heritage Plantation of Sandwich, is located at 67 Grove Street, Sandwich, Massachusetts. The public garden, with its nationally significant collection of rhododendrons hybridized by Charles Dexter, over 1,000 varieties of daylilies and extensive hosta collection, is complemented by three gallery buildings containing a world-class collection of American automobiles, American folk art and a working 1919 carousel and rare carousel figures.

The museum's grounds were once the estate of noted rhododendron hybridizer Charles O. Dexter, where between 1921 and 1943 Dexter developed between 5,000 and 10,000 seedlings annually. He planted many on the site. In 1969, Josiah K. Lilly III (1916–1995) and his wife established Heritage Plantation of Sandwich on the property.

Charles O. Dexter
Charles Owen Dexter (1862–1943) was an American rhododendron hybridizer. Using the Chinese species Rhododendron fortunei, he produced hybrids characterized by dense foliage, large stature and flowers of superior size and color, many of which were also fragrant. Notable examples of his work include Scintillation, Betty Hume, Parker's Pink, GiGi, Mrs. W.R. Coe, Wheatley and Westbury.

Between 1921 and 1943 Dexter carried on a massive breeding program at his 76-acre (310,000 m2) estate in Sandwich, Massachusetts. There he produced between 5,000 and 10,000 seedlings annually and gave thousands of plantings away to private gardens, nurseries and public botanical collections.

His estate is now operated as the Heritage Museums and Gardens which contains plantings of 125 of the known 145 Dexter cultivars.
Francis George (politician)
Kalambattuparambil Francis George is an Indian politician who is a member of the Kerala Congress. He is presently a member of 18th Lok Sabha representing Kottayam Lok Sabha constituency. He was a member of the 13th and 14th Lok Sabha, representing Idukki constituency of Kerala. He was formerly a leader of the Kerala Congress (M) and that of his former party Janadhipathya Kerala Congress.

Kerala Congress
Kerala Congress is an Indian political party founded in Kottayam, Kerala on 9 October 1964, by a block of former Indian National Congress leaders led by K. M. George. The party is primarily active in central Kerala. Initially its main support came from the Syrian Christians and the Nair community of southern Kerala.

The establishment of the Kerala Congress could be traced to the resignation and later death of P. T. Chacko, the Home Minister in the R. Sankar-led Congress ministry (1962–64). Fifteen rebel Congress Members of the Legislative Assembly subsequently supported a successful no confidence motion on the Sankar Ministry. K. M. George, R. Balakrishna Pillai and other leaders backed by the Syro-Malabar Catholic Church and the Nair Service Society leader Mannathu Padmanabhan, formed the "Kerala Congress" at Kottayam Thirunakkara Ground on 9th October 1964.
Gwgon ap Meurig
Gwgon ap Meurig (died c. 870/871) was a 9th-century king of Ceredigion and Ystrad Tywi (i.e., Seisyllwg) in southwest Wales.

Gwgon was the son of the former king Meurig ap Dyfnwallon and inherited the realm on the death of his father.

Gwgon's sister Angharad married King Rhodri the Great of Gwynedd. Gwgon is recorded by the annals as drowning around 871. The Chronicle of the Princes places his death in the entry for 870 and says he drowned crossing the River Llychwr in Gower while fighting Viking invaders.

Contrary to Welsh law, rule was then reported to have passed to Angharad's son Cadell as a subordinate king to his father.

Seisyllwg
Seisyllwg (Welsh: [sɛiˈsəɬʊɡ]) was a petty kingdom of medieval Wales. It is unclear when it emerged as a distinct unit, but according to later sources it consisted of the former Kingdom of Ceredigion plus the region known as Ystrad Tywi. Thus it covered the modern county of Ceredigion, part of Carmarthenshire, and the Gower Peninsula. It is evidently named after Seisyll, king of Ceredigion in the 7th or early 8th century, but it is unknown if he was directly responsible for its establishment. In the 10th century Seisyllwg became the centre of power for Hywel Dda, who came to rule most of Wales. In 920 Hywel merged Seisyllwg with the Kingdom of Dyfed to form the new kingdom of Deheubarth.