OpenLLM-France/wikimedia huggingface dataset:
# Using the Borsuk–Ulam Theorem

Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry is a graduate-level mathematics textbook in topological combinatorics. It describes the use of results in topology, and in particular the Borsuk–Ulam theorem, to prove theorems in combinatorics and discrete geometry. It was written by Czech mathematician Jiří Matoušek, and published in 2003 by Springer-Verlag in their Universitext series (ISBN 978-3-540-00362-5).

## Topics

The topic of the book is part of a relatively new field of mathematics crossing between topology and combinatorics, now called topological combinatorics. The starting point of the field, and one of the central inspirations for the book, was a proof that László Lovász published in 1978 of a 1955 conjecture by Martin Kneser, according to which the Kneser graphs $KG_{2n+k,n}$ have no graph coloring with $k+1$ colors. Lovász used the Borsuk–Ulam theorem in his proof, and Matoušek gathers many related results, published subsequently, to show that this connection between topology and combinatorics is not just a proof trick but an area.
The book has six chapters. After two chapters reviewing the basic notions of algebraic topology, and proving the Borsuk–Ulam theorem, the applications to combinatorics and geometry begin in the third chapter, with topics including the ham sandwich theorem, the necklace splitting problem, Gale's lemma on points in hemispheres, and several results on colorings of Kneser graphs. After another chapter on more advanced topics in equivariant topology, two more chapters of applications follow, separated according to whether the equivariance is modulo two or using a more complicated group action. Topics in these chapters include the van Kampen–Flores theorem on embeddability of skeletons of simplices into lower-dimensional Euclidean spaces, and topological and multicolored variants of Radon's theorem and Tverberg's theorem on partitions into subsets with intersecting convex hulls.

## Audience and reception

The book is written at a graduate level, and has exercises making it suitable as a graduate textbook. Some knowledge of topology would be helpful for readers but is not necessary. Reviewer Mihaela Poplicher writes that it is not easy to read, but is "very well written, very interesting, and very informative". And reviewer Imre Bárány writes that "The book is well written, and the style is lucid and pleasant, with plenty of illustrative examples."
Matoušek intended this material to become part of a broader textbook on topological combinatorics, to be written jointly with him, Anders Björner, and Günter M. Ziegler. However, this was not completed before Matoušek's untimely death in 2015.
# LNWR 1400 Class

The London and North Western Railway (LNWR) 1400 Class, commonly known as Bill Baileys after the popular little music hall number "Won't You Come Home Bill Bailey", was a class of 30 4-cylinder 4-6-0 compound locomotives. Essentially a Class B compound 0-8-0 with different wheel arrangement. 30 were built starting in 1903, intended for a mixed traffic role. The first was withdrawn in 1913, with several more following during the First World War, cannibalised to keep Class Bs running. None survived to the grouping of 1923; the last was withdrawn in 1921.
# Stretford Paddock F.C.

Stretford Paddock Football Club are an association football club based in Manchester, England.
The club's first team plays in the Cheshire Association Football League, League Two.

## Background

Stretford Paddock Football Club was set up by journalist and podcaster Stephen Howson, who current CEO and first team manager, out of a desire to practice the content of his journalism in real life. Howson runs a Manchester United F.C. fan channel, as well as being a co-presenter for "Full Time Devils" (now Stretford Paddock, in which the club gets its name). He has done journalism work in regards to Manchester United F.C. and other aspect of football for Soccer AM, BBC Sport, BT Sport, and Sky Sports, and co-presents "Vibe with Five" with Rio Ferdinand.

## History

Stretford Paddock was founded in 2020. As of 1 June 2022 the club has been fan owned.
First Silverware
On Saturday 8 July 2023, Stretford Paddock faced Droylsden FC in a significant match that marked Droylsden's return to football after three years of inactivity. The game, filled with anticipation, witnessed a delayed kickoff due to unexpected crowd congestion. In a dramatic turn of events, Stretford Paddock secured victory in a penalty shootout, lifting the Tony Downes Memorial Cup. This win, against a team that once held a notable position in the Northern Premier League, added the first silverware to Stretford Paddock's story.
Biggest League Win
Stretford Paddock FC recorded their largest league victory on 9 September 2023, when they defeated Wigan Town with a score of 10–0. This result stands out as the club's most significant win in league competition to date.

## Club Colours

The clubs colours are red and white with black socks. This is an homage to Manchester United, as the club is created by supporters of Manchester United. In 2021 the club announced a four-year partnership with Puma to supply kits.

## Home ground

The Paddock have been nomadic in terms of a home ground, having played home games at Droylsden FC's Butcher's Arms Ground for a part of the 2020–21 season. Flixton's Valley Road Stadium, Wright Robinson College and more recently Manchester Enterprise Academy have hosted Stretford Paddock home fixtures. Their current 2024-5 home ground is at Hyde United.
# Hucisko, Sucha County

Hucisko is a village in the administrative district of Gmina Stryszawa, within Sucha County, Lesser Poland Voivodeship, in southern Poland. It lies approximately 8 kilometres (5 mi) south-west of Stryszawa, 15 km (9 mi) south-west of Sucha Beskidzka, and 57 km (35 mi) south-west of the regional capital Kraków.
# Skull Valley School District

Skull Valley School District is a school district in Yavapai County, Arizona. It operates a single public K-8 school, Skull Valley Elementary School, in Skull Valley. The school has four teachers and generally 20–30 students. Enrollment in 2017 was 14 students.
As of 1976 the Prescott Unified School District takes secondary students from the Skull Valley district, as it is required to under law. The district operates Prescott High School.
The school district has leased land to the Skull Valley Historical Society, which has a museum next door to the school, and the historical school building itself is a significant historical structure in the area.
As of the 2003 census, the population in the Skull Valley Elementary School District was 525 people.
The school has two classrooms.

## Historical significance

Although official records do not indicate this, area settlers recall that a school was established in 1878. The school had been formally established by the early 1900s, when it offered education to children in all of the grades.
The two-room schoolhouse structure, built in 1925, still stands on the school grounds.
Despite extensive consolidations over time in Yavapai County, Arizona, Skull Valley still has a school. The new/current elementary school building sits on the same land, next to the historical schoolhouse. Students above the 8th grade are bused to Prescott to attend high school. The Prescott Unified School District operates Prescott High School.

## Programs

In 1988 it began participating in a county-led program to improve students' emotional well-being, aimed at school districts with total student populations under 600.
It participates in a track meet intended for low population schools in the area. The track meet, which Hillside Elementary School District, Kirkland Elementary School District, and Yarnell Elementary School District also participate in, began in 1957.
# Ryan Claridge

Ryan Quinlan Claridge (born April 12, 1981) is an American former professional football linebacker. He played in the National Football League (NFL) for the New England Patriots in the 2005 season, but was released early during 2006 training camp. He played college football at UNLV and is currently the owner of Big Apple Bagels in Traverse City, Michigan, which he purchased in May 2022.

## Early life

Claridge attended Almont High School in Almont, Michigan, and was a four-sport standout in football, tennis, basketball and track. In football, as a senior, he rushed for more than 1,300 yards and 27 touchdowns, was a first team All-Southern Thumb Association selection, was the League MVP and a first team All-State selection. He is the school record holder in rushing yards and rushing touchdowns, having played three years on the varsity team. In basketball, Claridge was the team's leading scorer and rebounder during his sophomore and senior seasons (he missed his junior season due to injury). In tennis, as a senior, he was also a first-team All-State selection. In track, as a junior, Claridge qualified for the state finals in the high jump and was also All-Southern Thumb Association in the 100-meter dash and the high jump.

## College and professional career

Claridge was recruited by College Football Hall of Famer John Robinson to the University of Nevada, Las Vegas as a linebacker for the Rebels football team. Claridge would play his entire eligibility at UNLV over five years, receiving a medical redshirt during the 2002 season due to a sports hernia.
Claridge was selected by the New England Patriots in the fifth round (170th overall) in the 2005 NFL draft. Claridge would spend the entire 2005 season on the team's practice squad before being cut during training camp in 2006.

## Personal life

Claridge's brother, the late Travis Claridge out of USC was a second round pick offensive lineman for the Atlanta Falcons in 2000.
After his professional football career was over, Claridge returned to southern Nevada and took up a coaching position with Coronado High School's Junior Varsity squad in 2007. The following season, Claridge would become the defensive coordinator for the varsity team at Del Sol High School and become a full-time teacher in the schools Driver's Education, Health and Physical Education Department. In 2011, Claridge left teaching/coaching to become a franchisee of Firehouse Subs in the Henderson/Las Vegas area. He owned and operated multiple Firehouse Subs before selling them after he moved back to Michigan. In 2015, he went back into education as a Physical Education teacher at Liberty High School and also served as the linebackers coach for Liberty's varsity football team.
Claridge was an investor in Philippi Sports Institute in Las Vegas, the institute is owned and operated by former World's Strongest Man finalist Mark Philippi. In May 2022, he purchased and locally operates a Big Apple Bagels franchise in Traverse City, Michigan.
# Şehzade Mehmed (son of Ahmed I)

Şehzade Mehmed (Ottoman Turkish: شہزادہ محمد; 11 March 1605 – 12 January 1621) was an Ottoman prince and the second son of Sultan Ahmed I, but his first with Kösem Sultan, Ahmed's favorite concubine, Haseki and probably legal wife.

## Life

Şehzade Mehmed was born on 11 March 1605 in Istanbul. He was the second son of his father Sultan Ahmed I and the first of his mother Kösem Sultan, Ahmed's Haseki sultan. In January 1609, Mehmed began his education under the guardianship of Hoca Ömer Efendi, together with his elder half brother, Şehzade Osman (future Sultan Osman II).
After his father's death in 1617, when Mehmed was twelve years old, his uncle Sultan Mustafa I ascended the throne. However, he was soon deposed and replaced by Osman in 1618.

## Death

Osman had asked the Şeyhülislam Hocazade Esad Efendi for an affirmative legal opinion to execute his brother. However, Esad Efendi refused to issue legal opinion. The Chief Judge of Rumeli Kemaleddin Efendi instead affirmed the execution of the prince. And so on 12 January 1621, Mehmed was executed. When the executioners were stretching rope in his neck he spoke:
   "Osman! I wish from Allah your reign get ruined, I hope you could not reign as much as what you have deprived me of my life!"
Twelve days following his death, a harsh snow fall in Istanbul which was considered as Allah’s message to Osman that he killed his brother. Osman ordered Mehmed's execution before leaving the capital for the Polish campaign.
He was buried beside his father in his mausoleum located in Blue Mosque, Istanbul.

## In popular culture

In 2015 Turkish historical fiction TV series Muhteşem Yüzyıl: Kösem, Şehzade Mehmed is portrayed by Turkish actor Burak Dakak.
# L'Éclipse (ski course)

L’Éclipse is a World Cup downhill ski course in Courchevel, France, opened in 2022. It was designed by Bruno Tuaire and Hannes Trinkl and built for the 2023 World Championships, and then has been hosting five men's alpine events.
In March 2022, it hosted the speed events of the World Cup finals for men and women.
The "Roc de Fer" ski course in nearby Méribel and L’Éclipse were co-hosting the World Championships in 2023.
This black course has a maximum incline of 31.4 degrees (61% gradient) and one of the steepest average inclines in the world with 16.7 degrees (30%), even more than dowhnill in Kitzbühel (27%) or Wengen (26%).
The start begins near Col de la Loze, while the finish area is adjacent to Tremplin du Praz, the ski jumping venue of the 1992 Winter Olympics.

## History

On 16 March 2022, this course originally intended for men only, was officially opened with both men's and women's downhill events, as the upper part of the "Roc de Fer" women's ski course in Méribel wasn't fully rebuilt yet.

## Events
### World Championships

| Year | Date | Event | Winner | Second place | Third place |
| ↓ Men ↓ ||||||
| 2023 | 7 February | AC | Alexis Pinturault | Marco Schwarz | Raphael Haaser |
| 2023 | 9 February | SG | James Crawford | Aleksander A. Kilde | Alexis Pinturault |
| 2023 | 12 February | DH | Marco Odermatt | Aleksander A. Kilde | Cameron Alexander |
| 2023 | 17 February | GS | Marco Odermatt | Loïc Meillard | Marco Schwarz |
| 2023 | 19 February | SL | Henrik Kristoffersen | AJ Ginnis | Alex Vinatzer |

### World Cup

| Season | Date | Event | Winner | Second place | Third place |
| ↓ Women ↓ ||||||
| 2021/22 | 16 March | DH | Mikaela Shiffrin | Christine Scheyer Joana Hählen | |
| 2021/22 | 17 March | SG | Ragnhild Mowinckel | Mikaela Shiffrin | Michelle Gisin |
| ↓ Men ↓ ||||||
| 2021/22 | 16 March | DH | Vincent Kriechmayr | Marco Odermatt | Beat Feuz |
| 2021/22 | 17 March | SG | Vincent Kriechmayr | Marco Odermatt | Gino Caviezel |

## Course sections

* Saut du Zenith – Mur du Son – Le S Des Arolles – Saut Des Jockeys – Le Trou Noir – Mur De La Bux – L'Envol – Le Mur Des Braves
# NSB Class 12

The NSB Type 12a, NSB Type 12b and NSB Type 12c were three steam locomotives built between 1891 and 1898 by Sächsische Maschinenfabrik and Dübs and Company for use on various railway lines in Norway. They were tank engines, which were useful so they wouldn't have to be turned around.

## History

The Norwegian railway lines, which were owned by the state, were administratively separate entities at the time. Locomotives were therefore permanently assigned to routes. It was not until July 1, 1920, that the Type 12 series steam locomotives, intended primarily for hauling local passenger trains, were officially assigned to the Oslo District.

### NSB Type 12a

12a no. 67 (Dübs 2846) was built for local trains between Kristiania and Ljan on the Smaalensbane (SB). The locomotive was ordered on November 18, 1890. After delivery in October 1891, she was put in service in November. It was fitted with a Bissel bogie at the front and an Adams axle at the rear, and was a high-pressure, saturated steam locomotive.
This was the same design as the NSB Type 11, which was being constructed and supplied at the same time by Dübs and Company.
The locomotive was withdrawn on March 24, 1952, and then scrapped.

### NSB Type 12b/12c

The other two locomotives—12c no. 100 and 12b no. 101—were ordered from the Sächsische Maschinenfabrik on February 23, 1897, and delivered on 1898 with factory numbers 2311 and 2311. From April 4, 1898, they were used on the Jaren–Røykenvik line belonging to the Kristiania–Gjøvikbanen (KGB) and had to run trains between Jaren and Røykenvik. Both locomotives were compound steam locomotives, unlike 12a no. 67. This locomotive type was further developed, and the successor was delivered to the Vossebane in 1904 as the Type 20.
12c no. 100 differed from 12b no. 101 slightly due to having larger water and coal capacity.
Both locomotives were put aside on October 25, 1951, Withdrawn on February 16, 1953, and then scrapped.
# Brandon Harkins

Brandon Daniel Harkins (born July 13, 1986) is an American professional golfer who currently plays on the Korn Ferry Tour. Harkins previously played on PGA Tour, PGA Tour Canada and PGA Tour Latinoamérica.

## Professional career

Harkins finished tied for 59th at the 2016 U.S. Open.
At the end of 2016, aged 30, Harkins finished 53rd in the Web.com Tour qualifying tournament. This earned him conditional status for the 2017 season. He finished his first Web.com Tour season in 21st place, and was promoted to the PGA Tour for 2018.
Harkins claimed his first professional victory in November 2021 at the TaylorMade Pebble Beach Invitational. He won by two shots ahead of Alex Čejka and Harry Hall.
In January 2022, Harkins won his first Korn Ferry tour event at The Bahamas Great Abaco Classic. Harkins won in a playoff over Dou Zecheng. This was Harkins' first win in 134 Korn Ferry starts.

## Professional wins (3)
### Korn Ferry Tour wins (1)

| No. | Date | Tournament | Winning score | Margin of victory | Runners-up |
| 1 | Jan 26, 2022 | The Bahamas Great Abaco Classic | −18 (69-65-68-68=270) | Playoff | Dou Zecheng |
Korn Ferry Tour playoff record (1–0)
| No. | Year | Tournament | Opponent | Result |
| 1 | 2022 | The Bahamas Great Abaco Classic | Dou Zecheng | Won with par on second extra hole |

### Gateway Tour wins (1)

* 2015 Winter 4

### Other wins (1)

| No. | Date | Tournament | Winning score | Margin of victory | Runners-up |
| 1 | Nov 21, 2021 | TaylorMade Pebble Beach Invitational | −21 (63-67-71-66=267) | 2 strokes | Alex Čejka, Harry Hall |
# Jeremiah Harman (judge)

Sir Jeremiah Le Roy Harman (13 April 1930 – 6 March 2021) was an English barrister and High Court judge. His judicial service was marred by a series of gaffes and high-profile incidents, culminating in his resignation in 1998 after being subject severe criticism by the Court of Appeal for delays in handing down a judgment.

## Early life

Harman was born on 13 April 1930 in Kensington, London, England, to Sir Charles Harman and Helen Sarah Le Roy Lewis. Harman was educated at Eton College, an all-boys public school (independent boarding school) in Berkshire.

### Military service

Following school, Harman joined the British Army in 1948 and was commissioned into the Royal Hampshire Regiment; he claimed to have served in the Coldstream Guards. On 4 May 1950, he transferred to the Parachute Regiment as a second lieutenant with seniority in that rank from 27 February 1949. He transferred to the Territorial Army as an acting lieutenant on 1 January 1951 with seniority from 1 December 1950, and was promoted to substantive lieutenant on 13 April 1953 with seniority from 1 December 1950. He transferred to the Territorial Army Reserve Of Officers on 14 October 1955, thereby ending his military service.

## Legal career

He was called to the bar at Lincoln's Inn in 1954. He was appointed a judge of the High Court's Chancery Division in 1982.
He was known for his comments which were taken to reinforce the popular public stereotype of judges being out of touch with everyday life. He claimed not to have heard of Oasis at the height of their fame in 1996, and not to be familiar with "Gazza" as the nickname for Paul Gascoigne in 1990 when he was the subject of media interest due to his performances at the 1990 World Cup.
When a female witness indicated that she preferred to be addressed as "Ms", Mr Justice Harman was reported to have said to her: "I've always thought there were only three kinds of women: wives, whores and mistresses."
In 1992 he tried to kick a taxi driver whom he mistook for a press photographer trying to take his briefcase.
Two of Harman's more notable decisions were:
* Cornhill Insurance plc v Improvement Services Ltd
* Breckland Group Holdings Ltd v London and Suffolk Properties
But he handed down a number of reported judicial decisions during his career.

## Resignation

He resigned his position in 1998 after being subject to severe criticism by the Court of Appeal for not handing down a judgment until 20 months after the hearing. For the year 2000 he served as Treasurer of Lincoln's Inn.

## Personal life

Harman married three times. He was married to Helen Gillian Wharton from 1955 to 1958. From 1960 to 1987 he was married to Erica Jane Bridgeman, daughter of the Hon. Sir Maurice Bridgeman. They had two sons and one daughter.
In 1987 he married thirdly, Katharine Frances Goddard Pulay (died 2002), daughter of the Rt. Hon. Sir Eric Sachs.
In 2021 Harman died in his home in Chelsea, London, after suffering from cancer.

## Arms

Coat of arms of Jeremiah Harman :
* NotesDisplayed at the Great Hall of Lincoln's Inn
# Slaton Independent School District

Slaton Independent School District is a public school district based in Slaton, Texas, United States. In addition to Slaton, the district serves students in rural southeastern Lubbock County and parts of Ransom Canyon. A small portion of extreme northeastern Lynn County lies within the district.
In 2009, the school district was rated "academically acceptable" by the Texas Education Agency.

## Schools

* Slaton High School (grades 9–12), 2008 National Blue Ribbon School
* Slaton Junior High School (grades 6–8)
* Cathelene Thomas Elementary School (grades 1–5)
* Austin Elementary School (pre-K–kindergarten)

## Notable students

* William John Cox, public interest attorney, author, and political activist; attended Slaton High School, 1956–57
# Verne S. Bennett

Vernon S. Bennett (January 1, 1867 – October 26, 1944) was an American college football coach. He served as the head football at Michigan State Normal School—now known as Eastern Michigan University—one season, in 1894, and compiling a record of 5–2.

## Early years

Bennett was born in Prattsburgh, New York to "Mr. and Mrs. E.N. Bennett". At the birth of his younger brother Clare in 1871, the family resided in Lapeer, Michigan. He enrolled at Michigan State Normal School in 1891, and while in school he served as president of the Normal Athletic Association, and as editor of the Atheneum Society. In 1892, he served as an enrolling and engrossing clerk for the Michigan House of Representatives. As a senior, he gave a commencement oration on international law, which is recorded as being "especially fine."

## Coaching career

Bennett was the fourth head football coach at Michigan State Normal School—now known as Eastern Michigan University—in Ypsilanti, Michigan, serving for one season, in 1894, and compiling a record of 5–2.

## Later life

Following his time as the football coach, Bennett resided in Fenton, Michigan with his family, and later in New Orleans. He died there in 1944.

## Head coaching record

| Year | Team | Overall | Conference | Standing |
| Michigan State Normal Normalites (Michigan Intercollegiate Athletic Association) (1894) ||||||
| 1894 | Michigan State Normal | 5–2 | 0–1 | 4th |
| Michigan State Normal: | Michigan State Normal: | 5–2 | 0–1 | |
| Total: | Total: | 5–2 | | |