OpenLLM-France/wikimedia huggingface dataset:
# Whitehead theorem

In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence. This result was proved by J. H. C. Whitehead in two landmark papers from 1949, and provides a justification for working with the concept of a CW complex that he introduced there. It is a model result of algebraic topology, in which the behavior of certain algebraic invariants (in this case, homotopy groups) determines a topological property of a mapping.

## Statement

In more detail, let X and Y be topological spaces. Given a continuous mapping
    $f\colon X\to Y$
and a point x in X, consider for any n ≥ 0 the induced homomorphism
    $f_{*}\colon \pi _{n}(X,x)\to \pi _{n}(Y,f(x)),$
where π$_n$(X,x) denotes the n-th homotopy group of X with base point x. (For n = 0, π$_0$(X) just means the set of path components of X.) A map f is a weak homotopy equivalence if the function
    $f_{*}\colon \pi _{0}(X)\to \pi _{0}(Y)$
is bijective, and the homomorphisms $f_{*}$ are bijective for all x in X and all n ≥ 1. (For X and Y path-connected, the first condition is automatic, and it suffices to state the second condition for a single point x in X.) The Whitehead theorem states that a weak homotopy equivalence from one CW complex to another is a homotopy equivalence. (That is, the map f: X → Y has a homotopy inverse g: Y → X, which is not at all clear from the assumptions.) This implies the same conclusion for spaces X and Y that are homotopy equivalent to CW complexes.
Combining this with the Hurewicz theorem yields a useful corollary: a continuous map $f\colon X\to Y$ between simply connected CW complexes that induces an isomorphism on all integral homology groups is a homotopy equivalence.

## Spaces with isomorphic homotopy groups may not be homotopy equivalent

A word of caution: it is not enough to assume π$_n$(X) is isomorphic to π$_n$(Y) for each n in order to conclude that X and Y are homotopy equivalent. One really needs a map f : X → Y inducing an isomorphism on homotopy groups. For instance, take X= S$^2$ × RP$^3$ and Y= RP$^2$ × S$^3$. Then X and Y have the same fundamental group, namely the cyclic group Z/2, and the same universal cover, namely S$^2$ × S$^3$; thus, they have isomorphic homotopy groups. On the other hand their homology groups are different (as can be seen from the Künneth formula); thus, X and Y are not homotopy equivalent.
The Whitehead theorem does not hold for general topological spaces or even for all subspaces of R$^n$. For example, the Warsaw circle, a compact subset of the plane, has all homotopy groups zero, but the map from the Warsaw circle to a single point is not a homotopy equivalence. The study of possible generalizations of Whitehead's theorem to more general spaces is part of the subject of shape theory.

## Generalization to model categories

In any model category, a weak equivalence between cofibrant-fibrant objects is a homotopy equivalence.
# James Storme

James Storme (born 12 April 1943) is a Belgian former football player and manager who played as a midfielder.
# Gigi Does It

Gigi Does It is an American sitcom that was created by David Krumholtz, Ricky Mabe, Zach Golden, Ben Newmark, and Dan Newmark, with Krumholtz playing a Jewish senior citizen (the title character) who learns she has inherited millions of dollars from her late husband. On April 28, 2015, IFC ordered the series. The series premiered on IFC on October 1, 2015. On December 5, 2015, the series was canceled by IFC.

## Cast

* David Krumholtz as Gigi
* Ricky Mabe as Ricky
* Lesley Ann Warren as Tretchy Feinberg

## Episodes

| No. | Title | Original release date | Prod. code | US viewers (millions) |
| 1 | "Glock Schlock" | October 1, 2015 (2015-10-01) | 101 | 42,000 |
| 2 | "Call Your Grandma" | October 8, 2015 (2015-10-08) | 102 | 20,000 |
| 3 | "Wart-A-Colors" | October 15, 2015 (2015-10-15) | 103 | 67,000 |
| 4 | "A Regular Kristy Yamatushy" | October 22, 2015 (2015-10-22) | 104 | N/A |
| 5 | "Eat Something" | October 26, 2015 (2015-10-26) | 105 | 144,000 |
| 6 | "Let's Get Schvitzical" | November 2, 2015 (2015-11-02) | 106 | 75,000 |
| 7 | "Whine" | November 9, 2015 (2015-11-09) | 107 | N/A |
| 8 | "Love Thyself" | November 16, 2015 (2015-11-16) | 108 | 81,000 |

## Reception

On Rotten Tomatoes, the series has an aggregate score of 29% based on 2 positive and 7 negative critic reviews.
# 2010 Mongolian Premier League

Statistics of Mongolian Premier League in the 2010 season.

## Overview

Khangarid won the championship.

## League standings

| Pos | Team | Pld | W | D | L | GF | GA | GD | Pts | Qualification |
| 1 | Khangarid | 6 | 4 | 1 | 1 | 13 | 5 | +8 | 13 | Qualify for Group A |
| 2 | Mazaalai | 6 | 4 | 1 | 1 | 12 | 7 | +5 | 13 | Qualify for Group B |
| 3 | Erchim | 6 | 3 | 2 | 1 | 9 | 6 | +3 | 11 | Qualify for Group A |
| 4 | Khoromkhon | 6 | 2 | 1 | 3 | 6 | 10 | −4 | 7 | Qualify for Group B |
| 5 | Ulaanbaatar University | 6 | 2 | 0 | 4 | 9 | 12 | −3 | 6 | Qualify for Group A |
| 6 | Selenge Press | 6 | 2 | 0 | 4 | 12 | 18 | −6 | 6 | Qualify for Group B |
| 7 | Khasiin Khulguud | 6 | 1 | 1 | 4 | 11 | 14 | −3 | 4 | |

## Group A standings

| Pos | Team | Pld | W | D | L | GF | GA | GD | Pts | Qualification |
| 1 | Ulaanbaatar University | 2 | 1 | 0 | 1 | 3 | 1 | +2 | 3 | Qualified for semi-finals |
| 2 | Khangarid | 2 | 1 | 0 | 1 | 2 | 3 | −1 | 3 | Qualified for semi-finals |
| 3 | Erchim | 2 | 1 | 0 | 1 | 1 | 2 | −1 | 3 | |

## Group B standings

| Pos | Team | Pld | W | D | L | GF | GA | GD | Pts | Qualification |
| 1 | Selenge Press | 2 | 2 | 0 | 0 | 7 | 3 | +4 | 6 | Qualified for semi-finals |
| 2 | Mazaalai | 2 | 1 | 0 | 1 | 4 | 3 | +1 | 3 | Qualified for semi-finals |
| 3 | Khoromkhon | 2 | 0 | 0 | 2 | 3 | 8 | −5 | 0 | |

## Play-offs
### Bracket

| Semi-finals | Semi-finals | Final | Final |
| Ulaanbaatar University | 1 (4) |
| Mazaalai (pen.) | 1 (5) | | |
| Mazaalai (pen.) | 1 (5) | Mazaalai | 1 |
| | | Khangarid | 2 |
| Selenge Press | 2 | Khangarid | 2 |
| Khangarid | 3 | | |
| Khangarid | 3 | Third-place | Third-place |
| | | Ulaanbaatar University | 2 (4) |
| | | Selenge Press (pen.) | 2 (5) |
# Cardiff Athletics Stadium

The Cardiff Athletics Stadium (also known as Leckwith Athletics Stadium) was an athletics and football stadium in Cardiff, Wales. It opened in 1989 and was demolished in 2007, replaced by the Cardiff International Sports Stadium.
The Cardiff Grange Quins of the Welsh Football League and the Cardiff City F.C. reserve and ladies teams used the available facilities. The athletics track had a synthetic surface measuring 400 metres with 8 circular lanes and 10 straight lanes. It had been open to the public, seating 2,613 (covered) with changing rooms and all-weather floodlights.

## History

The stadium was opened in 1989. When it was built, the £5.5m stadium was considered to be suitable for the 1994 Commonwealth Games if Cardiff had hosted it.
The athletes to have competed at the stadium included Linford Christie, Colin Jackson, and Jamie Baulch.
The stadium has now been demolished to make way for the Cardiff City Stadium, which is part of the Leckwith development and also retail units as part of the development. A new athletics facility has been built just across the Leckwith Road about 100 metres away as part of the same development, it is known as the Cardiff International Sports Stadium.
# Little Miss Atlanta

Little Miss Atlanta is an American reality television series which aired on TLC in 2016. A spin-off of Toddlers and Tiaras, it profiles contestants in the Little Miss Black US Pageant system, based in Atlanta, Georgia. Each episode features three young African-American girls and their mothers as they compete in one of the system's pageants.

## Episodes

| Ep # | Total | Title | Airdate |
| 1 | 1 | "Southern Belles & Mama Drama" | October 5, 2016 (2016-10-05) |
| 2 | 2 | "Leave It On The Floor" | October 12, 2016 (2016-10-12) |
| 3 | 3 | "Eat, Sleep, "BLEEP", Pageants!" | October 26, 2016 (2016-10-26) |
| 4 | 4 | "Pageant Dad Duel" | November 2, 2016 (2016-11-02) |
# Mavelikara Krishnankutty Nair

Mavelikkara Krishnankutty Nair (11 October 1920 – 13 January 1988) was a Carnatic Mridangam player. He received his training from Alleppey Venkappan Pillai and Veechur Krishna Iyer. He considered Palani Subramaniam Pillai as his 'Manasa Guru'. He received the Padma Shri from the President of India. He received the Kerala Sangeetha Nataka Akademi Award in 1971 and the Kerala Sangeetha Nataka Akademi Fellowship in 1980. Krishnankutty Nair was also an artiste for All India Radio in Trivandrum.
# Griswold Memorial Young Women's Christian Association

The Griswold Memorial Young Women's Christian Association, today known as the YWCA Center for Women, is a historic YWCA building in Downtown Columbus, Ohio. It was built in 1929 and was listed on the National Register of Historic Places in 1993. Renovations took place in 1963-64 and 1984. The building was named for Charles C. Griswold, and was a gift of his wife Mary, who donated about $400,000 to the YMCA's building fund.
The eight-story tower is built in the Second Italian Renaissance Revival style. It has a brick foundation, two stories of rusticated limestone, and an upper six stories of brick. There are five belt courses wrapping around the building.
# Grooms Tavern Complex

Grooms Tavern Complex is a historic tavern located at Grooms Corners in Saratoga County, New York. The complex consists of the tavern, a wagon and blacksmith shop, and a frame privy. The tavern building was built about 1825 and is a 2-story, timber-framed, gable-roofed building in a vernacular Federal style. It consists of a main block with 1+1⁄2-story, frame kitchen wing in the rear. When expanded to two stories in the 1840s, a Greek Revival style cornice was added. The building was partially remodeled in the late 19th and early 20th centuries. The tavern building was also operated as a general store. The wagon and blacksmith shop was constructed in the 1840s and is a 2-story, rectangular, timber-framed building with a gable roof in the Greek Revival style.
It was listed on the National Register of Historic Places in 2000.
# Grubb Mansion

Grubb Mansion is an historic home which is located in the High Street Historic District, in Pottstown, Montgomery County, Pennsylvania.
It was added to the National Register of Historic Places in 2003.

## History and architectural features

Built in 1906, Grubb Mansion is a three-story, asymmetrical, brownstone building, which was designed in the Queen Anne style. Located in Pottstown's High Street Historic District, it features a nine-foot-deep front porch with an open turret, art glass windows and an octagonal tower.
The dwelling was converted to office use in 1954 and a union hall was added to the rear in 1956.
It was added to the National Register of Historic Places in 2003.
# Maliwan Prabnarong

Maliwan Prabnarong (Thai: มลิวรรณ ปราบณรงค์, born 27 August 1990) is a Thai indoor volleyball. With her club Bangkok Glass she competed at the 2016 World Club Championship.

## Awards
### Individuals

* 2013–2014 Thailand League "Best opposite spiker"

### Clubs

* 2014–2015 Thailand League - Champion, with Bangkok Glass
* 2015 Thai-Denmark Super League - Champion, with Bangkok Glass
* 2015 Asian Club Championship - Champion, with Bangkok Glass
* 2015–2016 Thailand League - Champion, with Bangkok Glass
* 2016 Thai-Denmark Super League - Champion, with Bangkok Glass
* 2016–17 Thailand League - Runner-up, with Bangkok Glass
* 2017 Thai-Denmark Super League - Runner-up, with Bangkok Glass
* 2017–18 Thailand League - Third, with Bangkok Glass
* 2018 Thai-Denmark Super League - Runner-up, with Bangkok Glass
# Mighell, Queensland

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Mighell is a rural locality in the Cassowary Coast Region, Queensland, Australia. In the 2021 census, Mighell had a population of 363 people.

## Geography

The locality is bounded by the South Johnstone River to the east and by its tributary Bamboo Creek to the west and north.
The Bruce Highway enters the locality from the east (South Innisfail) crossing the South Johnstone River on the Centenary Bridge. Once in Mighell, the highway travels north along River Avenue, and then exits the locality to the north (Innisfail) crossing Bamboo Creek on an unnamed bridge.
The North Coast railway line enters the locality from the south (Mundoo) and exits to the north-west (Goondi Hill) crossing Bamboo Creek. There are no railway stations in the locality.
The land use is predominantly growing sugarcane and there is a network of cane tramways to transport the harvested sugarcane to the South Johnstone sugar mill in South Johnstone to the south. There is also grazing on native vegetation in the north-west of the locality.
The land use in the north and north-east of the locality is more suburban in character being an extension of the urban area of Innisfail to the north.

## History

The locality was named after Innisfail solicitor and businessman Norman Mighell.
Innisfail State High School opened on 24 January 1955 and operated until the end of 2009 at 2 Stitt Street (17°32′12″S 146°01′41″E﻿ / ﻿17.5367°S 146.0280°E﻿ / -17.5367; 146.0280﻿ (Innisfail State High School (former))). In 2010, it was amalgamated with the Innisfail Inclusive Education Centre (a special education facility) and Tropical North Queensland TAFE (Innisfail Campus) to form Innisfail State College using the site of the TAFE campus at Innisfail Estate. Innisfail State High School's website was archived.

## Demographics

In the 2016 census, Mighell had a population of 380 people.
In the 2021 census, Mighell had a population of 363 people.

## Education

There are no schools in Mighell. The nearest government primary schools are Innisfail State School in neighbouring Innisfail to the north and Mundoo State School in neighbouring Mundoo to the south. The nearest government secondary school is Innisfail State College in Innisfail Estate to the north-east.

## Amenities

The Innisfail Conservatorium of Music (also known as the Con Theatre) is a performing arts centre at 5 River Avenue (17°32′02″S 146°01′49″E﻿ / ﻿17.5339°S 146.0304°E﻿ / -17.5339; 146.0304﻿ (CONSERVATORIUM OF MUSIC)).
Innisfail Cultural Complex is a community centre off River Avenue (17°32′01″S 146°01′44″E﻿ / ﻿17.5337°S 146.0289°E﻿ / -17.5337; 146.0289﻿ (INNISFAIL CULTURAL COMPLEX)).
Innisfail Cemetery is at 8 Scullen Avenue (17°31′54″S 146°01′39″E﻿ / ﻿17.5316°S 146.0276°E﻿ / -17.5316; 146.0276﻿ (Innisfail Cemetery)). It is operated by the Cassowary Coast Regional Council.
# The Wasp (1918 film)

The Wasp is a lost 1918 silent film comedy drama directed by Lionel Belmore and starring stage star Kitty Gordon. It was produced by William A. Brady and distributed by World Film Company.

## Cast

* Kitty Gordon as Grace Culver
* Rockliffe Fellowes as Harry Cortland/Tim Purcell
* Charles Gerry as John Culver (*note: this may be Charles Cherry)
* Zadee Burbank as Mrs. Culver (*as Sadee Burbank)
* William Calhoun as Mr. Cortland
* Edward Roseman as Jackson Devereaux
* Victor Kennard as Kane Putnam
* Lionel Belmore as Brazsos
* Hazel Washburn as Miller, the Maid
* Edmund Burns as Harry's Roommate (*as Edward Burns)
# Jawahar Navodaya Vidyalaya, Mothuka, Faridabad

Jawahar Navodaya Vidyalaya, Mothuka, Faridabad is a school in Ballabgarh tehsil, Faridabad district of Haryana, India. It is part of the Jawahar Navodaya Vidyalaya system of alternate schools for gifted students in India.

## Geography

Jawahar Navodaya Vidyalaya, Mothuka is geographically situated around 24 km (15 mi). away from Faridabad at a small village known as Mothuka in a 32-acre (13 ha) campus.

## Management

This school is managed by Navodaya Vidyalaya Samiti which is an autonomous organization of the Ministry of Human Resource Development. Main affairs of the school are looked after by NVS regional office Chandigarh. On state level Deputy commissioner of the concerned district is the Chairman of the Vidyalaya level Committees with local educationists, public representatives and officials from the District as members.

## Admission procedure

Talented students from each district are selected through an All India Level Entrance Exam conducted each year by CBSE and are given admission to the 6th standard/class in the JNVs of respective districts. Till 1998, the Jawahar Navodaya Vidyalaya Selection Test (JNVST) was conducted by the National Council of Educational Research and Training, however it is conducted by the Central Board of Secondary Education ever since. The test is largely non-verbal and objective in nature and is designed to prevent any disadvantage to children from rural areas. Now admissions are also taken in Class IX and XI. During academic year 2008-09 admissions will be allowed in Class VIII. These admissions are conducted through an objective and descriptive test containing questions on English, Mathematics, Science, & Social Sciences. This "Lateral Entry" system is devised to fill the vacancies that arise due to withdrawal of admissions of the children who are admitted in class VI.

## Affiliations

JNV Mothuka is affiliated with Central Board for Secondary Education C.B.S.E. The school follows syllabus prescribed by CBSE.
# Jeremy Ayers

Jeremy Ayers (1948 – October 24, 2016) was an American artist, writer, photographer, and musician.
A member of the Athens, Georgia creative community, Ayers was a Warhol superstar under the name Sylva Thinn early in his career and wrote a column for Andy Warhol's Interview magazine. He published three books of photography, and co-wrote songs for The B-52's and R.E.M. In 2021, a newly discovered species of ant (Strumigenys ayersthey) was named in his honor.

## Life and death

Born Charles Jerry Ayers, he grew up in Athens, Georgia. His father Robert H. Ayers was a civil rights advocate and taught theology at the University of Georgia.
By the early 1970s, Ayers became involved with Andy Warhol's Factory as the androgynous "Sylva Thinn" (also written as "Silva Thin") and he wrote a column for Interview magazine. He also appeared in David Bailey's 1973 documentary on Warhol.
In the late 1970s, Ayers returned to Athens and he was a drummer in the band Limbo District. Ayers was credited as co-writer of "52 Girls" from The B-52's 1979 debut album. He also worked with fellow Athens musicians R.E.M., co-writing the song "Old Man Kensey" from the 1985 album Fables of the Reconstruction.
Ayers published three books of photography (Aeronautica, 2011; Today in New York, 2011; and Occupy!, 2012), which featured scenes from Athens, New York City street life, and Occupy Wall Street.
Ayers died of a seizure at the age of 68 on October 24, 2016.

## Legacy

Following his death, the Athens Institute for Contemporary Art presented a month-long exhibition featuring Ayers's work titled "Out There: Photographs in the spirit of Jeremy Ayers." In addition to photographs taken by Ayers, the exhibit included photography done by other artists taken "in the same spirit" of his work.
In 2017 Ayers's friend Michael Stipe presented an art installation in his honor at Moogfest in Durham, North Carolina. The installation, titled "Jeremy Dance," featured footage of Ayers dancing to a 120 beats per minute disco song; Stipe then paired the dancing footage with music specially composed (using a Moog synthesizer and a Roland Juno) to match Ayers's movements.
In 2021 German entomologist Phillip Hoenle discovered a new species of ant, which he sent to Yale University taxonomic expert Douglas Booher. After receiving the blessing of Stipe, Booher decided to name the ant Strumigenys ayersthey after Ayers. The "they" in ayersthey refers to the singular they "in a celebration of gender diversity." According to Booher, Ayers himself identified as a gay man; the "they" suffix was intended to honor both Ayers's LGBT activism and the non-binary community.
# USP Controlled Room Temperature

The USP Controlled Room Temperature is a series of United States Pharmacopeia guidelines for the storage of pharmaceuticals; the relevant omnibus standard is USP 797. Although 100% compliance remains challenging for any given facility, the larger protocol may be regarded as constituting a form of clean room which is included in a suite of best practices.
# Shafaat Ahmed Khan

Ustad Shafaat Ahmed Khan (20 May 1954 – 24 July 2005) New Delhi, India, was one of the leading tabla maestros in the field of Hindustani classical music.
Shafaat Ahmed Khan came from the "Dilli Gharana" (Delhi gharana) and was the son and disciple of tabla maestro Ustad Chhamma Khan who was a prominent exponent of the Dilli Gharana. Shafaat Ahmed Khan was famous for his mastery over clear 'bols' and melodious tone of the tabla, accompaniment (sangat) and systematic improvisation. During his active years he was one of the leading tabla maestros of India. Shafaat Ahmed Khan was a recipient of "Padma Shree" award in 2003.
He performed concerts all around the world with classical artistes like Ravi Shankar, Nikhil Banerjee, Shivkumar Sharma, Amjad Ali Khan, Bhimsen Joshi, Jasraj, Hari Prasad Chaurasia, Kishori Amonkar, Birju Maharaj, besides performances as solo artist. Shafaat Ahmed Khan also played various taal vadya kacheris and jugalbandis with carnatic artists like Vikku Vinayakram, Lalgudi Jayaraman, Balamurali Krishna, Vellore Ramabhadran, Sivamani, Shankar Mahadevan and others, internationally. Shafaat Ahmed Khan was popular among artists because of his humble nature and down to earth attitude.

## Awards and recognition

Shafaat Ahmed Khan was a recipient of the fourth highest Indian civilian award, "Padma Shri" in 2003.

## Death

He died at age 51 on 24 July 2005 after being diagnosed with acute Hepatitis-B.
# Roti (disambiguation)

Roti is a flatbread originating from the Indian subcontinent.
Roti or ROTI may also refer to:
* Roti (1942 film), an Indian Hindi-language film directed by Mehboob Khan
* Roti (1974 film), an Indian Hindi-language film directed by Manmohan Desai
* Roti (1988 film), a Pakistani Punjabi-language film directed by Idrees Khan
* Roti (album), an album by Gurdas Maan
* Rate of turn indicator, a navigational instrument on a ship
* Return on time invested, a productivity and efficiency metric
* "Rôti" (Hannibal), an episode of the television series Hannibal
* Rote Island, Indonesia
* Roti languages, a group of Timoric languages
* Roti dialect, a Bajaw language dialect
* Roti (wrap), a wrap style sandwich

## People with the surname

* Fred Roti (1920–1999), American politician