OpenLLM-France/wikimedia huggingface dataset:
# Simplicial approximation theorem

In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation) approximated by ones that are piecewise of the simplest kind. It applies to mappings between spaces that are built up from simplices—that is, finite simplicial complexes. The general continuous mapping between such spaces can be represented approximately by the type of mapping that is (affine-) linear on each simplex into another simplex, at the cost (i) of sufficient barycentric subdivision of the simplices of the domain, and (ii) replacement of the actual mapping by a homotopic one.
This theorem was first proved by L.E.J. Brouwer, by use of the Lebesgue covering theorem (a result based on compactness). It served to put the homology theory of the time—the first decade of the twentieth century—on a rigorous basis, since it showed that the topological effect (on homology groups) of continuous mappings could in a given case be expressed in a finitary way. This must be seen against the background of a realisation at the time that continuity was in general compatible with the pathological, in some other areas. This initiated, one could say, the era of combinatorial topology.
There is a further simplicial approximation theorem for homotopies, stating that a homotopy between continuous mappings can likewise be approximated by a combinatorial version.

## Formal statement of the theorem

Let $K$ and $L$ be two simplicial complexes. A simplicial mapping $f:K\to L$ is called a simplicial approximation of a continuous function $F:|K|\to |L|$ if for every point $x\in |K|$, $|f|(x)$ belongs to the minimal closed simplex of $L$ containing the point $F(x)$. If $f$ is a simplicial approximation to a continuous map $F$, then the geometric realization of $f$, $|f|$ is necessarily homotopic to $F$.
The simplicial approximation theorem states that given any continuous map $F:|K|\to |L|$ there exists a natural number $n_{0}$ such that for all $n\geq n_{0}$ there exists a simplicial approximation $f:\mathrm {Bd} ^{n}K\to L$ to $F$ (where $\mathrm {Bd} \;K$ denotes the barycentric subdivision of $K$, and $\mathrm {Bd} ^{n}K$ denotes the result of applying barycentric subdivision $n$ times.), in other words, if $K$ and $L$ are simplicial complexes and $f:|K|\to |L|$ is a continuous function, then there is a subdivision $K'$ of $K$ and a simplicial map $g:K'\to L$ which is homotopic to $f$. Moreover, if $\epsilon :|L|\to {\mathbb {R}}$ is a positive continuous map, then there are subdivisions $K',L'$ of $K,L$ and a simplicial map $g:K'\to L'$ such that $g$ is $\epsilon$-homotopic to $f$; that is, there is a homotopy $H:|K|\times [0,1]\to |L|$ from $f$ to $g$ such that $\mathrm {diam} (H(x\times [0,1]))<\epsilon (f(x))$ for all $x\in |K|$. So, we may consider the simplicial approximation theorem as a piecewise linear analog of Whitney approximation theorem.
# Sitavva Joddati

Sitavva Joddati is a Karnataka-based social activist working for the emancipation and empowerment of women suffering within the Devadasi system. In 2018, she was conferred the Padma Sri, the fourth highest civilian award, by the President of India.

## Early life

Joddati was born in Kabbur village of Chikkodi Taluk in the Indian state of Karnataka. The youngest of six daughters, Sitavva was "promised" as a Devadasi to the community by her parents who believed that by doing this, they would be rewarded with a son.
After undergoing a religious ritual at the age of 7, Sitavva was made a Devadasi. By age 17, she had borne three children.

## Career

Sitavva met Latamala, the Managing Director of Women Development Corporation, in 1991 who made her realise how degrading the practice of Devadasi was to the dignity of women. Sitavva decided to save herself from the Devadasi system. She and the other Devadasis who used to travel to southern Maharashtra and northern Karnataka to attend religious fairs began to speak up against the practice, and within a week, the number of dissenters had risen to 45 women.
Soon after, Sitavva joined the Mahila Abhivrudhi Samrakshana Sansthe (MASS), an organisation dedicated to the eradication of the Devadasi system. Since then, she has rescued over 4,000 women and rehabilitated them with other jobs. She joined MASS when she was 17 and for over three decades, she has worked to uplift Devadasis and Dalits in Belgaum, Karnataka.
She is the CEO of MASS organisation since 2012. The organisation has around 4000 former Devadasis as members. Joddati conduct aids and legal workshops and programmes on women and child rights, financial management, STDs and other issues. She has created over 300 self-help groups (SHG) that provide financial support to former Devadasis, through banks and micro-lenders.

## Recognition

In March 2018, Joddati was conferred the fourth highest civilian honour of India, the Padma Sri, by the President of India, Ram Nath Kovind.
# Six Arches, Ackworth

The Six Arches is a railway viaduct in Ackworth, West Yorkshire, England, named after its design. It carries the Pontefract to Rotherham line over the River Went.
The viaduct was constructed for the Swinton and Knottingley Joint Railway, which opened in 1879. It remains in use as part of the Dearne Valley line although traffic is rather limited and a speed limit of 30mph is in force, probably to stop the mortar falling out.
Ackworth used to have a station, but it was shut down and demolished. The goods sheds still remain and have been converted into a private residence.
# Sindre Walstad

Sindre Walstad is a Norwegian handball player.
He made his debut on the Norwegian national team in 1994, and played 85 matches for the national team between 1994 and 2006. He competed at the 2005 World Men's Handball Championship.
# Simun

Simun and variants may refer to:

## Places

* Simun, Burma
* Simun, Iran

## People

* Šimun, a given name in Croatia and a surname in Croatia and Slovakia
* Símun (fl. 1350), head of state of the Faroe Islands
* Símun Mikkjal Zachariasen (1853–1931), Faroese teacher and social activist
* Símun Petur Zachariasen (1887-1977), Faroese teacher, editor, and politician
* Símun av Skarði (1872-1942), Faroese poet, politician and teacher
* Jóan Símun Edmundsson (born 1991), Faroese professional footballer
# Sivakasi block

Sivakasi block is a revenue block in the Virudhunagar district of Tamil Nadu, India. It has a total of 54 panchayat villages.
# Sivakasi Municipal Corporation

Sivakasi City Municipal Corporation is the civic body governing city of Sivakasi in Indian state of Tamil Nadu. Municipal Corporation mechanism in India was introduced during British Rule with formation of municipal corporation in Madras (Chennai) in 1688, later followed by municipal corporations in Bombay (Mumbai) and Calcutta (Kolkata) by 1762. Sivakasi City Municipal Corporation is headed by Mayor of city and governed by Commissioner.

## History and administration

Sivakasi Municipal Corporation in Virudhunagar district was formed in year 2021 and is one of the 21 municipal corporations in Tamil Nadu. The place is known majorly for manufacturing fire crackers.
Sivakasi City Municipal Corporation a Commissioner Mayor, a Council, a Standing Committee, a Wards Committee for facilitating various works.
Currently the Municipal Commissioner is .

## Factors driving Sivakasi City Municipal Corporation

Sivakasi City Municipal Corporation is driven by following factors:
* Population Growth.
* Increase in annual Income.
* Improvement of Roads.
* Providing drinking water.
* Improving landscape.
* Improving employment opportunities.
* Improving relations between police and public.
* Waste Management.
* Arranging facilities during natural calamities.
* Establishing industrial units.
* Providing sewage connection.

## Sivakasi City Municipal Corporation local body polls

Sivakasi City Municipal Corporation will get a mayor and municipal council through local body polls.
# Sisingaan

Sisingaan, also known as Gotong Singa, Singa Ungkleuk, Singa Depok, Kuda Ungkleuk, Pergosi, or Odong-odong, is a traditional Sundanese lion dance that originated in Subang, West Java, Indonesia. This lion dance performance is marked by a form of an ark or palanquin that resembles a lion. The lion ark or lion-shaped effigy is carried by a group of dancers who perform various attractions accompanied by traditional music. This dance is usually performed to celebrate a child's circumcision ceremony, where the child is carried on the lion around the kampung (village).

## Etymology

In Sundanese language the term sisingaan means "imitation lion", "playing the lion" or "lion play". This refers to the form of a lion-like effigy that is the main part of the show.

## Form

Unlike other lion dances however, this lion dance is quite different. It uses lion-like statue or an effigy doll that resembles a lion in couchant (lying down) position, being held in a palanquin-like structure by four or two men with bamboo rods. The lion statue is ridden by the children who have been circumcised, carried away and held high by men in certain dance movements, sometimes involving acrobatics. The dance is accompanied with a traditional music troupe consists of musicians playing musical instruments; including kendang (drum), kempul, gong, suling bamboo flute and trumpet.

## History

At first, the Sundanese people of Subang had an art called "oesungan" which they carried in the form of birds, deer, stealth on a stretcher. At that time there was no stretcher in the form of a lion like this time. Then The Sisingaan was created around 1975 by Sundanese artists, because remembering the arrival of the reog Ponorogo art to the city which was brought by urbanites from Ponorogo.
After the Sundanese artists discussed with the Reog artists who were very different from the Reog Dog-Dog Sundanese, that reog from East Java attracted more attention and had philosophical values and historical records against Dutch colonialism, an art was created that was able to show the distinctive identity of Subang from the ideas of the artist.
Sisingaan was inspired by the Reog series in East Java, which tells of the joy of the journey of King Singa Barong's bodyguards from the kingdom of Lodaya to the Daha kingdom. Even though the king was known to be cruel and arrogant, the guards were always loyal to carry the litter that King Singa Barong slept with.
In addition, as a symbol of the resistance of the people of Subang against Dutch arbitrariness, which is depicted as a lion in the VOC symbol, it is intended as a calming historical learning education for students.
At first, the Sundanese people of Subang had an art called "oesungan" which they carried in the form of birds, deer, stealth on a stretcher. At that time there was no stretcher in the form of a lion like this time

## Gallery

* Sisingaan dance performance in a village.
* Sisingaan dance with kids riding the lion effigy.
* Sisingaan lion dance parade during Independence day parade in 2008 Merdeka Square, Jakarta.
# Situation Room (disambiguation)

The Situation Room is a conference room and intelligence management center in the White House.
Situation Room may also refer to:
* Situation Room (photograph), a 2011 photograph by Pete Souza, taken in the White House Situation Room during the killing of Osama bin Laden
* The Situation Room with Wolf Blitzer, an afternoon newscast on CNN
* The Situation Room, a 2024 book by George Stephanopoulos
# Sjötofta

Sjötofta is a village situated in Tranemo Municipality, Västra Götaland County, Sweden with 208 inhabitants in 2005.
# Sjöstrand

Sjöstrand may refer to:
* Arnold Sjöstrand (1903–1955), Swedish actor and film director
* Carl Eneas Sjöstrand (1828–1906), Swedish sculptor
* Johan Sjöstrand (born 1987), Swedish handballer
* Johannes Sjöstrand (born 1947), Swedish mathematician
* Östen Sjöstrand (1925–2006), Swedish poet, writer and translator
* Sven-Erik Sjöstrand, born 1954, is a Swedish Left Party politician, member of the Riksdag 1998–2006
* Tore Sjöstrand (born 1921), former Swedish athlete, winner of 3000 m steeplechase at the 1948 Summer Olympics
# Skabo Jernbanevognfabrikk

Skabo Jernbanevognfabrikk was a mechanical workshop focusing on design and construction of railcars. It was established by Hans Skabo in Drammen, Norway, in 1864; it became the first rail car factory in the country when it took delivery of the cars for Kongsvingerbanen. Due to the size of the venture, it moved to Tyskerstranden at Skøyen in Kristiania (now Oslo) in 1873.
Because the delivery of rail cars is uneven, Skabo participated in other manufacturing, including coachworks for trucks, buses and taxicabs. The first Norwegian-produced trolleybus was delivered from Skabo in 1911. Also technical devices and stalls and in 1926 firewood powered snow melters; the latter contraption rather unsuccessful. In 1948 the company was bought by Norsk Elektrisk & Brown Boveri (NEBB), who sold it to Strømmens Værksted in 1959; moving all activity to Strømmen and closing the Skøyen plant.

## Stock

Skabo has built the chassis the NSB El 6 and NSB El 7 electric locomotives delivered to Rjukanbanen, for locomotives no. 5 and 6 on Thamshavnbanen, and for the multiple units type 62, type 65, type 66, type 67, type 68 and type 88. The electrical components for these were often built by Norsk Elektrisk & Brown Boveri or foreign companies like AEG or ASEA.
Many of the wooden passenger cars delivered to both Norges Statsbaner and others are built by Skabo. This included the cars delivered to Urskog-Hølandsbanen and Nesttun-Osbanen. For NSB the models included A11, A20, A21, B2, B3, B9, B20, B23, B30, B31, DF37, F2, F3, F20, R1, R20, WLAB, WLB and ZU21.
For Oslo Sporveier Skabo built several trams, including models KSS 32, KSS 95, KSS96, Hkb 42, EB 1001, EB 1007, OS 397, Hkb 110, EB 1013, Hkb 205, OS 166, OS 170 and EB 1011.
In Trondheim Skabo delivered one tram of TS Class 1 in addition to TS Class 2 and TS Class 5 for Trondheim Sporvei and GB Class 2 for A/S Graakalbanen.
# Siren (magazine)

Siren was a bimonthly Canadian magazine, published in Toronto, Ontario, for the city's lesbian community.

## History and profile

The magazine was launched in 1995 by a women's collective of volunteers. Its popularity increased in late 1996, around the time the lesbian monthly magazine Quota ceased publication. It underwent a controversial editorial revamp in 2002, ending its association with its regular contributors in favour of a more freelance story and contribution structure. The magazine was quoted in a discussion paper released by the Ontario Human Rights Commission about extending rights for transsexuals. One of the columns that appeared regularly in the magazine was titled "Dykes n' tykes".
Noted contributors to the magazine included Sheila Cavanagh, Debra Anderson, and Billie Jo Newman.
The magazine ceased publication in 2004 due to financial problems.
# Skinker

Skinker may refer to:
* Alexander R. Skinker (1883–1918), Medal of Honor Recipient during World War I
* Skinker/DeBaliviere, St. Louis, neighborhood of St. Louis, Missouri
* Skinker (St. Louis Metrolink), subway station at the intersection of Skinker Boulevard and Forest Park Parkway
* Wydown/Skinker, St. Louis, neighborhood in St. Louis, Missouri
# Sleepwalking (Maria Lawson song)

"Sleepwalking" is the debut single from The X Factor UK series 2 finalist, Maria Lawson.
The song features a sample of the Chi-Lites hit single "Have You Seen Her".
The track was released on 14 August 2006 and charted at number 20 on the UK Singles Chart. That same week, fellow series 2 finalist Chico also released a single. However, Lawson's track charted four places higher. "Sleepwalking" generally received positive criticism in the UK and was A-listed on BBC Radio 2. To date, the song has sold over 35,000 copies in the UK alone. The single was the first and only track to be lifted from Lawson's debut album Maria Lawson.
"Sleepwalking" also charted at number 44 in Ireland and at number 67 in Australia. The Australian release was released only as a download single. The single's B-side is a cover of James Blunt's "You're Beautiful".

## Charts

| Chart | Peak position |
| UK Singles Chart | 20 |
| Irish Singles Chart | 44 |
| Australian Singles Chart | 67 |
# Siyak

Siyak may refer to:
* Siyaka, a 10th-century Paramara king of central India
* Sihag, a clan of India
* Tonb-e Siyak, a village in Iran
# Slab, West Virginia

Slab is an unincorporated community in Ritchie County, West Virginia, United States.
# Toriko Chiya

Toriko Chiya (Japanese: 稚野鳥子, Hepburn: Chiya Toriko, born August 25 in Tokyo) is a Japanese manga artist. She is best known for Clover as well as Tokyo Alice.

## Works

* Danchi Kaidan Kaidan (団地階段会談) (1990, Bouquet, Shueisha, 1 volume)
* Bara-gara no Hoshī Toshigoro (薔薇柄の欲しい年頃) (1991, Bouquet, Shueisha, 2 volumes)
* Miracle (1992–1993, Bouquet, Shueisha, 4 volumes)
* Watashi no Ichiban Sukina Hito (わたしの一番好きな人) (1993, Bouquet, Shueisha, 1 volume)
* Angel ni Kiite (天使（エンジェル）に聞いて, Enjeru ni Kiite) (1993–1994, Bouquet, Shueisha, 4 volumes)
* Tengoku no Hana (天国の花) (1994–1996, Bouquet, Shueisha, 6 volumes)
* Clover (クローバー, Kurōbā) (1997–2010, Bouquet→Cookie→Chorus, Shueisha, 24 volumes)
* Tokyo Alice (東京アリス, Tōkyō Arisu) (2005–2015, Kiss, Kodansha, 15 volumes)
* Kazoku Switch (家族スイッチ, Kazoku Suitchi) (2010–2012, Chorus→Cocohana, Shueisha, 4 volumes)
* Clover trèfle (クローバー trefle(トレフル), Kurōbā Torefuru) (2012–ongoing, Cocohana, Shueisha, 8 volumes)
* Tsuki to Yubisaki no Aida (月と指先の間) (2015–ongoing, Kiss, Kodansha, 3 volumes)
# Tomoxia lineella

Tomoxia lineella is a species of beetle in the genus Tomoxia of the family Mordellidae. It was described by John Lawrence LeConte in 1862.
# Washington Trust Field and Patterson Baseball Complex

Washington Trust Field and Patterson Baseball Complex is a college baseball park in the northwest United States, located on the campus of Gonzaga University on Spokane, Washington. Opened seventeen years ago in 2007, it is the home venue of the Gonzaga Bulldogs of the West Coast Conference (WCC).
Designed by architect ALSC Architects, Washington Trust Field and Patterson Baseball Complex has 1,300 fixed seats in the main seating bowl and a total capacity of 2,300. The complex includes field lighting, home and visitors locker rooms, baseball offices, laundry, training and equipment facilities, batting cages, a natural grass field, modern restrooms and concession stands for the convenience of the fans, and an electronic information board and a stone marker welcoming visitors. The playing field is aligned southeast at an elevation just under 1,900 feet (580 m) above sea level; the site was formerly an annex of the U.S. Postal Service.
Patterson Baseball Complex is named after the family of Michael Patterson (class of 1969), chairman of Gonzaga's Board of Trustees and a major contributor to the project. Washington Trust Field is named after Washington Trust Bank in which, Pete Stanton, the chairman and CEO of Washington Trust Bank, and Jack Heath, president of Washington Trust Bank, were the major forces behind the field naming.
The Bulldogs played on campus from 1968 through 2003 at August/ART Stadium (Pecarovich Field until 1996), which was displaced by the construction of McCarthey Athletic Center, home of the Gonzaga basketball teams. After ground was broken for McCarthey in April 2003, the baseball team finished the season at Spokane Falls Community College, then played three seasons in Spokane's minor league venue, Avista Stadium.
A few hundred yards south of the old field, ground was broken for the facility in June 2006, and it opened nine months later on March 15, 2007, a 9–4 victory over Rider University. The first night game was played April 17, a 4–7 loss to Washington State; the dedication game was three nights later, a 6–3 conference victory over Saint Mary's.
# Mussorgsky (disambiguation)

Modest Mussorgsky (1839–1881) was a Russian composer.
Mussorgsky can also refer to:
* The Mussorgsky family of Russian nobility
* Mussorgsky (film), a 1950 Soviet film about the composer

## Mussorgskij

* Mussorgskij (crater), crater on Mercury
# Mylappapuram

Mylappapuram is a small village located in Tirunelveli district. Mylappapuram has many temples and churches. Temple festivals are grantly celebrated every year. The Tamilnad Mercantile Bank Limited Vengadampatti Branch is located here. A church, which has been renovated and is nearly 100 years old, is located in Mylappapuram. A tasmac bar is also located here. It has a bus stand named kamarajar bus stand. Large water tanks supply thamirabarani water all over the village.
Mylappapuram is 17 km (11 mi) from Kutralam, 25 km (16 mi) from Papanasam and 7 km from pavoorchatram. Mylappapuram, a small village is surrounded by many natural resources and waterfalls like Kutralam falls, Papanasam dam, Ramanathi dam, Kadananathi dam. Thamirabarani is the biggest and perennial river and it support 2 districts. But it is unable to supply water to Mylappapuram, and it is 30 km (19 mi) from the Pothigai mountain.

## Mylappapuram

* Mylappapuram
* South Mylappapuram
* Rajakkalkudiyirupu
* Arunthathiyar colony (East Street)
* Kamaraj Nagar

## Streets of Mylappuram

* North Street, (CSI street) Church of South India), RC Church street, North street
* West Street,
* South Street,
* East Street

## Places of Mylappapuram

* Subramaniya swami Temple
* Roman Catholic church - Assi church
* Mylappapuram Tuesday Market
* Avvaiyar amman temple
* Mupputathi amman temple
* St. Andrew's church [Church of South India]
* south mylappuram amman Temple
* south mylappuram ramar Temple
* south mylappuram kalaswami Temple
* South mylappuram sudalai madaswami temble
* St. Thomas Church { Church Of South India}
* Naddu st amman kovil mylappapuram
* Poi kaatha Sudali Mada Swamy
* Thirumal Iyyan Temple

## Sports teams

* ANV stars mylai ( cricket Team)
* chain Gang Group, Mylai. [cricket Team]
* Mylai cool guys
* New 11 stars
* shadow boys in south mylai
* Rajakudiyiruppu royal challengers (Rrc cricket)
* 7 Nanbargal [Kabadi Team]
* Action Boys
* Fire Friends [Cricket Team]
* Star kings group, Rajakudiyiruppu{cricket team}

## Festivals

* Vaikasi visagam,
* Pankuni Uthiram
* Pongal
* thirukarthigai deepam,
* This Tirunelveli district location article is a stub. You can help Wikipedia by expanding it.
* v
* t
* e