OpenLLM-France/wikimedia huggingface dataset:
# Sequentially compact space

In mathematics, a topological space X is sequentially compact if every sequence of points in X has a convergent subsequence converging to a point in $X$.
Every metric space is naturally a topological space, and for metric spaces, the notions of compactness and sequential compactness are equivalent (if one assumes countable choice). However, there exist sequentially compact topological spaces that are not compact, and compact topological spaces that are not sequentially compact.

## Examples and properties

The space of all real numbers with the standard topology is not sequentially compact; the sequence $(s_{n})$ given by $s_{n}=n$ for all natural numbers $n$ is a sequence that has no convergent subsequence.
If a space is a metric space, then it is sequentially compact if and only if it is compact. The first uncountable ordinal with the order topology is an example of a sequentially compact topological space that is not compact. The topological product of $2^{\aleph _{0}}={\mathfrak {c}}$ copies of the closed unit interval is an example of a compact space that is not sequentially compact.

## Related notions

A topological space $X$ is said to be limit point compact if every infinite subset of $X$ has a limit point in $X$, and countably compact if every countable open cover has a finite subcover. In a metric space, the notions of sequential compactness, limit point compactness, countable compactness and compactness are all equivalent (if one assumes the axiom of choice).
In a sequential (Hausdorff) space sequential compactness is equivalent to countable compactness.
There is also a notion of a one-point sequential compactification—the idea is that the non convergent sequences should all converge to the extra point.
# Garrett's Island House

Garrett's Island House is a historic home located near Plymouth, Washington County, North Carolina. It was built about 1760, and is a 1+1⁄2-story, Georgian / Federal style frame dwelling with a gambrel roof. It has a shed roofed front porch and double-shouldered exterior brick chimney. Garrett's Island House is thought to be the oldest extant dwelling in Washington County.
It was listed on the National Register of Historic Places in 2001.
# Choi In-young

Choi In-young (born 5 March 1962) is a former South Korean football player who played as a goalkeeper.
He played mostly for Ulsan Hyundai Horang-i. He participated for South Korea national football team at two editions of FIFA World Cup in 1990 and 1994, retiring from international football following the final group stage match in the latter tournament, against Germany, played in Dallas under a stifling 46°C heat, which led him to request his substitution by future national starter Lee Woon-jae at half-time.

## Playing career

He played in South Korea for Seoul City (1981–1983) on an amateur basis, Kookmin Bank FC (1983) and Ulsan Hyundai Horang-i (1984–1996).

## Coaching career

He was goalkeeper coach at Ulsan Hyundai Horang-i (1997–2003), Kyungil University (2005) and Jeonbuk Hyundai Motors (2006–2013).

## Career statistics
### International clean sheets

    Results list South Korea's goal tally first.
| # | Date | Venue | Opponent | Result | Competition |
| 1 | 6 June 1983 | Suwon, South Korea | Thailand | 4–0 | 1983 President's Cup |
| 2 | 8 June 1983 | Seoul, South Korea | Nigeria | 1–0 | 1983 President's Cup |
| 3 | 12 June 1983 | Jeonju, South Korea | Indonesia | 3–0 | 1983 President's Cup |
| 4 | 15 June 1983 | Seoul, South Korea | Ghana | 1–0 | 1983 President's Cup |
| 5 | 2 March 1985 | Kathmandu, Nepal | Nepal | 2–0 | 1986 FIFA World Cup qualification |
| 6 | 19 May 1985 | Seoul, South Korea | Malaysia | 2–0 | 1986 FIFA World Cup qualification |
| 7 | 28 July 1990 | Beijing, China | Japan | 2–0 | 1990 Dynasty Cup |
| 8 | 29 July 1990 | Beijing, China | North Korea | 1–0 | 1990 Dynasty Cup |
| 9 | 5 September 1990 | Seoul, South Korea | Australia | 1–0 | Friendly match |
| 10 | 23 September 1990 | Beijing, China | Singapore | 7–0 | 1990 Asian Games |
| 11 | 27 September 1990 | Beijing, China | China | 2–0 | 1990 Asian Games |
| 12 | 1 October 1990 | Beijing, China | Kuwait | 1–0 | 1990 Asian Games |
| 13 | 5 October 1990 | Beijing, China | Thailand | 1–0 | 1990 Asian Games |
| 14 | 7 June 1991 | Seoul, South Korea | Egypt | 0–0 | 1991 President's Cup |
| 15 | 14 June 1991 | Seoul, South Korea | Australia | 0–0 (4–3 PSO) | 1991 President's Cup |
| 16 | 16 June 1991 | Seoul, South Korea | Egypt | 2–0 | 1991 President's Cup |
| 17 | 22 August 1992 | Beijing, China | Japan | 0–0 | 1992 Dynasty Cup |
| 18 | 26 August 1992 | Beijing, China | China | 2–0 | 1992 Dynasty Cup |
| 19 | 27 September 1993 | Seoul, South Korea | Australia | 1–0 | Friendly match |
| 20 | 16 October 1993 | Doha, Qatar | Iran | 3–0 | 1994 FIFA World Cup qualification |
| 21 | 28 October 1993 | Doha, Qatar | North Korea | 3–0 | 1994 FIFA World Cup qualification |
| 22 | 23 June 1994 | Boston, United States | Bolivia | 0–0 | 1994 FIFA World Cup |

## Honours
### Club

Ulsan Hyundai
* K League 1: 1996
* Korean League Cup: 1986, 1995

### International

South Korea
* Dynasty Cup: 1990
# Binary asteroid

A binary asteroid is a system of two asteroids orbiting their common barycenter. The binary nature of 243 Ida was discovered when the Galileo spacecraft flew by the asteroid in 1993. Since then numerous binary asteroids and several triple asteroids have been detected.
The mass ratio of the two components – called the "primary" and "secondary" of a binary system – is an important characteristic. Most binary asteroids have a large mass ratio, i.e. a relatively small satellite in orbit around the main component. Systems with one or more small moons – also called "companions" or simply "satellites" – include 87 Sylvia, 107 Camilla and 45 Eugenia (all triples), 121 Hermione, 130 Elektra (a quadruple), 22 Kalliope, 283 Emma, 379 Huenna, 243 Ida and 4337 Arecibo (in order of decreasing primary size). Some binary systems have a mass ratio near unity, i.e., two components of similar mass. They include 90 Antiope, 2006 VW$_{139}$, 2017 YE5 and 69230 Hermes, with average component diameters of 86, 1.8, 0.9 and 0.8 km, respectively.
In August 2024 Gaia reported 352 new binary asteroid candidates.

## Description

Several theories have been posited to explain the formation of binary-asteroid systems. Many systems have significant macro-porosity (a "rubble-pile" interior). The satellites orbiting large main-belt asteroids such as 22 Kalliope, 45 Eugenia or 87 Sylvia may have formed by disruption of a parent body after impact or fission after an oblique impact. Trans-Neptunian binaries may have formed during the formation of the Solar System by mutual capture or three-body interaction. Near-Earth asteroids, which orbit in the inner part of the Solar System, most likely form by spin-up and mass shedding, likely as a result of the YORP effect. Numerical simulations suggest that when solar energy spins a “rubble pile” asteroid to a sufficiently fast rate by the YORP effect, material is thrown from the asteroid's equator. This process also exposes fresh material at the poles of the asteroid.

## Gallery

* Time-lapse video of binary main-belt comet 2006 VW$_{139}$ (288P)
* Artist's impression of the double asteroid 90 Antiope
# Witt algebra

In mathematics, the complex Witt algebra, named after Ernst Witt, is the Lie algebra of meromorphic vector fields defined on the Riemann sphere that are holomorphic except at two fixed points. It is also the complexification of the Lie algebra of polynomial vector fields on a circle, and the Lie algebra of derivations of the ring C[z,z$^{−1}$].
There are some related Lie algebras defined over finite fields, that are also called Witt algebras.
The complex Witt algebra was first defined by Élie Cartan (1909), and its analogues over finite fields were studied by Witt in the 1930s.

## Basis

A basis for the Witt algebra is given by the vector fields $L_{n}=-z^{n+1}{\frac {\partial }{\partial z}}$, for n in $\mathbb {Z}$.
The Lie bracket of two basis vector fields is given by
    $[L_{m},L_{n}]=(m-n)L_{m+n}.$
This algebra has a central extension called the Virasoro algebra that is important in two-dimensional conformal field theory and string theory.
Note that by restricting n to 1,0,-1, one gets a subalgebra. Taken over the field of complex numbers, this is just the Lie algebra ${\mathfrak {sl}}(2,\mathbb {C} )$ of the Lorentz group $\mathrm {SO} (3,1)$. Over the reals, it is the algebra sl(2,R) = su(1,1). Conversely, su(1,1) suffices to reconstruct the original algebra in a presentation.

## Over finite fields

Over a field k of characteristic p>0, the Witt algebra is defined to be the Lie algebra of derivations of the ring
    k[z]/z$^p$
The Witt algebra is spanned by L$_m$ for −1≤ m ≤ p−2.
# Isabel Larrañaga Ramírez

Isabel de Larrañaga Ramírez, HCSCJ (19 November 1836 - 17 January 1899) known as Isabel of the Heart of Jesus was a Filipino-Mestiza (mixed-race Spaniard) religious sister and foundress who is venerated in the Catholic Church. She was born in Manila, Philippines. Her beatification process is currently underway.

## Life

Isabel de Larrañaga was born in Manila, Philippines, on 19 November 1836, to Juan Andrés Ma. de Larrañaga (the Military Governor of Manila at that time) and Isabel Ramírez Patiño. Her father was from Spain, and her mother was born of Spanish descent in Lima, Peru. They were married in Huancayo, Peru.
She was the youngest of ten children. Her parents were Spanish and she was a Filipina by birth and by virtue of citizenship. She was baptized in San Miguel de Arcángel in Malacañan 30 days after her birth.
After the death of her father in 1838, her mother returned to Spain with the children. Ramírez spent her childhood and early adolescence in Madrid and in Lima. Her mother ensured that Ramírez received a good education, learning music, painting, and languages (French, English, and Italian).
In 1855, Ramírez accompanied her mother and brother, Francisco Adrian, to Lima, Peru. There, the eighteen-year-old Ramírez became a teacher and engaged in charity work. She visited patients in hospitals, and became a catechist for children and young people. Seven years later, she and her mother went returned to Spain, and they resided in Madrid.

## Death

In 1894 Ramírez sent a religious expedition to Cuba in spite of the delicate political situation during that time. During her second trip to Cuba, she suffered from heart problems which were aggravated with sufferings from the war, which eventually led to her death on 17 January 1899. She left a flourishing institute that, after her death, has extended on the following nations: Puerto Rico, Venezuela, Peru, and Chile.

## Cause of beatification

On 17 December 1982 her beatification cause was formally opened by Pope John Paul II; thereby, bestowing upon her the title of "Servant of God Isabel Larrañaga Ramírez" ("Isabel of the Heart of Jesus"). Seventeen years later on 26 March 1999, Ramírez was elevated to venerable by Pope John Paul II.
# Hydroscapha natans

Hydroscapha natans is a species of skiff beetle in the family of Hydroscaphidae. It is found in North America.
# WI Sports

WI Sports is a local sports channel that broadcasts on channel 14 on the Flow Trinidad cable system serving Trinidad. It is a cable only channel dedicated to airing local and regional sporting events, leagues, news highlights and live feeds of games. Its headquarters are located at Ground Floor, Nicholas Towers, Independence Square, Port of Spain.

## History

On 1 April 2010, WI Sports replaced Tempo TV due to low viewership. On Sunday 1 April 2012, Tempo TV returned to Flow's channel lineup.

## Network Slogans

* Bringing local sports to your homes. (2011–present)
# Nanyang Crescent MRT station

Nanyang Crescent MRT station is a future elevated Mass Rapid Transit (MRT) station on the Jurong Region line in Western Water Catchment, Singapore. The station will be located within the Nanyang Technological University (NTU).

## History

On 9 May 2018, the Land Transport Authority (LTA) announced that Nanyang Crescent station would be part of the proposed JRL. The station will be constructed as part of Phase 3, consisting of 7 stations – a 4 station extension to Jurong Pier from Boon Lay and a 3 station extension to Peng Kang Hill from Tawas. It was expected to be completed in 2028. However, the restrictions on construction due to the COVID-19 pandemic has led to delays, with the completion date pushed to 2029.
The contract for the design and construction of the Nanyang Gateway and Nanyang Crescent stations and 1.4 km (0.87 miles) of associated viaducts – Contract J113 – was awarded to Hwa Seng Builder Pte Ltd at S$263 million (US$192.8 million) on 6 April 2021. Construction is scheduled to start in the second quarter of 2021, with expected completion in 2029.
Starting on 31 July 2022, a section of Nanyang Drive had to be temporarily diverted for the station's construction, with two bus stops along the road shifted accordingly. The overhead bridge connecting the Nanyang Technological University (NTU) North Spine and the National Institute of Education (NIE) was demolished on 11 September that year.

## Details

Nanyang Crescent station will serve the JRL and will be located between the Nanyang Gateway and Peng Kang Hill stations. The official station code will be JW4. The station will be located in the Nanyang Technological University (NTU), along Nanyang Drive near the junction with Nanyang Walk.
# Fowler-Steele House

The Fowler-Steele House, also known historically as Ivy Hall, is a historic house on North Main Street in Windsor, Vermont, United States. Built in 1805 and restyled about 1850, it has an architecturally distinctive blend of Federal and Greek Revival styles. It served for many years as a local church parsonage. It was listed on the National Register of Historic Places in 1982.

## Description and history

The Fowler-Steele House stands on the northern fringe of Windsor's main village, on the east side of North Main Street just north of Hubbard Brook. Oriented facing south, it is a 2+1⁄2-story painted brick structure, with a gabled roof and brick foundation. Chimneys are located on the outside of the north and south elevations, an unusual placement for Vermont because snow sliding from the roof can apply pressure to them. The main facade is five bays wide, with a center entrance that is slightly recessed and topped by a transom window. The interior follows a typical Georgian central hall plan, with nearly identical parlors on either side of a central hall, and the kitchen at the northeast corner. The parlors, each accessed by pocket doors, have elaborate Greek Revival trim, while the kitchen and northwest room retain more modest Federal period features. A 1+1⁄2-story brick ell extends to the rear.
The house was built about 1805 for Bancroft Fowler, the fourth minister of the Windsor Congregational Church, and is located near the site of the first European settlement in what is now Windsor. Fowler gave the house to the church congregation upon his departure from the post in 1819, and it served as the church parsonage until 1835, after which it was sold to the Baptist congregation and became their parsonage. Jason Steele, a local banker, bought the house in 1848, and added the then-fashionable Greek Revival features to the interior and exterior. In 1897 it was purchased by Will Davis, a railroad conductor, who improved its landscaping and dubbed it "Ivy Hall". In the 1960s it was converted for use as a medical office, with modernized interiors, but it has since then returned to residential use and had its interior restored.
# Jinma Road station

Jinma Road is a station on Line 3 of the Dalian Metro in Liaoning Province, China. It is located in the Jinzhou District of Dalian City.
# 1961 U.S. National Championships (tennis)

The 1961 U.S. National Championships (now known as the US Open) was a tennis tournament that took place on the outdoor grass courts at the West Side Tennis Club, Forest Hills in New York City, United States. The tournament ran from September 1 until September 10, 1961. It was the 81st staging of the U.S. National Championships, and the fourth Grand Slam tennis event of 1961.

## Finals
### Men's singles

Roy Emerson defeated Rod Laver 7–5, 6–3, 6–2

### Women's singles

Darlene Hard defeated Ann Haydon 6–3, 6–4

### Men's doubles

Chuck McKinley / Dennis Ralston defeated Rafael Osuna / Antonio Palafox 6–3, 6–4, 2–6, 13–11

### Women's doubles

Darlene Hard / Lesley Turner defeated Edda Buding / Yola Ramírez 6–4, 5–7, 6–0

### Mixed doubles

Margaret Smith / Bob Mark defeated Darlene Hard / Dennis Ralston default
# Ollie Taylor

Oliver Harold Taylor (born March 7, 1947) is an American former professional basketball player. A 6-foot-2-inch (1.88 m) guard/forward, Taylor played college basketball at the University of Houston from 1968 until 1970. More recently, he was placed in charge of New Business for Milton Keynes-based agency elliotts.
Taylor was selected by the Cleveland Cavaliers in the 12th round of the 1970 NBA draft. Although he did not see action in the NBA, he went on to play in four ABA seasons with the New York Nets, San Diego Conquistadors, and Carolina Cougars.
Born in New York City, Taylor rode the bench in high school before jumping center against Kareem Abdul-Jabbar in college and playing against Julius Erving and Rick Barry in the ABA. Along the way, he set numerous National Junior College Athletic Association (NJCAA) records while leading San Jacinto to the 1968 national title. Taylor followed that up by lifting Houston to a Sweet 16 appearance in 1970. Taylor had a 46-inch (1.2 m) vertical leap, which he used for dunking.
# Amylyx Pharmaceuticals

Amylyx Pharmaceuticals, Inc is a biopharmaceutical company headquartered in Cambridge, Massachusetts. Amylyx is best known for AMX0035, an experimental therapy for amyotrophic lateral sclerosis. AMX0035 was approved for medical use in Canada as Albrioza, in June 2022, and in the United States, as Relyvrio, in September 2022. It was withdrawn in April, 2024.

## History

Amylyx Pharmaceuticals was founded in 2013 by Joshua Cohen and Justin Klee when the two were undergraduate students at Brown University. The two proposed that taurursodiol and sodium phenylbutyrate together might prevent dysfunction of mitochondria and the endoplasmic reticulum, safeguarding neurons. Klee and Cohen were advised by Rudolph E. Tanzi, who ultimately served as the founding chair of Amylyx's scientific research board. After Klee and Cohen were able to achieve strong results in pre-clinical research, Tanzi connected the two to his colleagues at Massachusetts General Hospital, which culminated in clinical trials and FDA approval. The company was granted $2.2 million by the ALS Association with funds raised through the Ice Bucket Challenge.
Amylyx went public in January 2022. The company's shares began trading on the Nasdaq on January 7, 2022 under the symbol AMLX.
After a disappointing Phase 3 trial of AMX0035 failed to produce significant differences versus a placebo, on April 4, 2024 Amylyx announced they would begin the process of withdrawing Albrioza and Relyviro from the North American market. Amylyx received praise for keeping its pre-approval promise to stop selling the drug if it turned out to be ineffective, an unusually ethical move which the FDA rarely requires. The company cited its independence from major pharmaceutical companies as a reason it could do so.
# Maize Craze

Maize Craze was the game in the inaugural year, 1992, of the FIRST Robotics Competition. Gameplay consists of four individual robots, or “machines”, trying to collect tennis balls, or “treasure”, into their own home base. The field also includes an impediment to the robots consisting of a layer of loose corn kernels covering the entire playing field, 1-2 inches deep.

## Field and Scoring

Maize Craze is played on a 16 feet (4.9 m) by 16 feet square piece of plywood, 2.5 feet (0.8 m) above the floor, covered in a 1-2 inch deep layer of loose corn kernels. The field's perimeter is rimmed with 8 inch (20.3 cm) tall Plexiglas walls. The four home bases measure 20 inches (50.8 cm) square and one is placed at the center of each of the four edges of the field.
There are five posts on the field, one in each corner and one in the center. The center post is 12 inches (30.5 cm) tall and is capped by a high-value tennis ball worth 25 points. Two of the corner posts, at a diagonal from the other, are 36 inches (91.5 cm) tall and capped by high-value tennis balls. The remaining two corner posts are 24 inches (61 cm) tall and capped by medium-value tennis balls worth 10 points. 150 low-value tennis balls worth 1 point are placed around the center post. Robots remove high- and medium- value tennis balls from the posts and score them along with low-value tennis balls collected from the floor into their respective home bases.
A structure extends 25 feet (7.6 m) above the floor to support the electrical umbilicals for the robots.

### Game Pieces

The only game piece in Maize Craze is the “treasure”, or tennis balls. There are a total of 155 available during a game, all staged on the field. Three high-value balls are staged on three of the posts, two medium-value balls are staged on the other posts, and 150 low-value balls are staged on the ground around the center post.

### Scoring Areas

Each robot has a corresponding home base where they score game pieces and also where they are staged at the beginning of the match. To score, robots must remove tennis balls from the posts or retrieve them from the floor and place them into their home base. The winner of each match is determined by the total point value of the tennis balls in each home base.

## Robots

Robots are powered and controlled through 'umbilicals' hanging from the overhead structure and a 9-volt on-board "transistor radio" battery. The robots must fit within a 38 cm (15 in) by 50 cm (19.7 in) by 34 cm (13.4 in) box and weigh no more than 11 kg (24.3 lb). The robot could only be driven by two student members of the team, although an “engineer”, or mentor, is allowed to coach from within a designated coaching box.