OpenLLM-France/wikimedia huggingface dataset:
# Igor Costrov

Igor Costrov (born 3 August 1987) is a Moldovan footballer who plays for BATE Borisov.

## Club career

Costrov began his professional career with FC Dinamo Bender in Moldova before signing with Liga Leumit club Hapoel Be'er Sheva. He signed with Major League Soccer club Kansas City Wizards in February 2010. However, Kostrov was released by the club without making a league appearance. He joined Belarusian club Slavia Mozyr in January 2016.

## International career

He made his debut for Moldova national football team on 3 June 2021 in a friendly against Turkey. He substituted Alexandru Antoniuc in the 67th minute.
# Matt Dooley

Matt Dooley (born April 16, 1996) is an American professional stock car racing driver who has previously competed in the ARCA Menards Series from 2018 to 2019.
Dooley has also previously competed in series such as the Southern All Star Dirt Racing Series, the Crate Racin' USA Dirt Late Model Series, the Crate Racin' USA $100,000 Challenge, and the World of Outlaws Late Model Series.

## Motorsports results
### ARCA Menards Series

(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led.)
ARCA Menards Series results :
| Year | Team | No. | Make | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | AMSC | Pts |
| 2018 | Fast Track Racing | 11 | Toyota | DAY | NSH | SLM 23 | TAL | TOL | CLT | POC | MCH | MAD | | | | | | | | | | | | 73rd | 245 |
| 2018 | Fast Track Racing | 10 | Toyota | | | | | | | | | | GTW 20 | CHI | IOW | ELK | POC | ISF | BLN | DSF | SLM | IRP | KAN | 73rd | 245 |
| 2019 | Fast Track Racing | 11 | Ford | DAY | FIF 18 | SLM | TAL | NSH | TOL | CLT | POC | MCH | MAD | GTW | CHI | ELK | IOW | POC | ISF | DSF | SLM | IRP | KAN | 74th | 140 |
# Kyle Lockrow

Kyle Lockrow (born May 5, 1990) is an American professional stock car racing driver who has competed in the ARCA Menards Series.
Lockrow has also previously competed in the NASCAR Advance Auto Parts Weekly Series.

## Motorsports results
### ARCA Menards Series

(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led.)
ARCA Menards Series results :
| Year | Team | No. | Make | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | AMSC | Pts | Ref |
| 2021 | Vanco Racing | 66 | Ford | DAY | PHO | TAL | KAN | TOL | CLT | MOH | POC | ELK | BLN | IOW | WIN | GLN | MCH | ISF | MLW | DSF | BRI | SLM | KAN 21 | 106th | 23 | |
# Lexi Gay

Lexi Gay (born January 12, 2001) is an American professional stock car racing driver who has competed in the ARCA Menards Series.
Gay has also previously competed in the Southern National Late Model Series, Southeast Limited Late Model Series, the Paramount Kia Big 10 Challenge, the Thursday Thunder Legends Racing Series, and the NASCAR Advance Auto Parts Weekly Series.

## Motorsports results
### ARCA Menards Series

(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led.)
ARCA Menards Series results :
| Year | Team | No. | Make | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | AMSC | Pts | Ref |
| 2019 | Empire Racing | 44 | Ford | DAY | FIF | SLM | TAL | NSH 19 | TOL | CLT | POC | MCH | MAD | GTW | CHI | ELK | IOW | POC | ISF | DSF | SLM | IRP | KAN | 76th | 135 | |
# Richard Hauck

Richard Hauck (born January 23, 1963) is an American professional stock car racing driver who has previously competed in the ARCA Racing Series from 1992 to 2017.
Hauck has previously competed in the Super Cup Stock Car Series.

## Motorsports results
### ARCA Racing Series

(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led.)
ARCA Racing Series results :
| Year | Team | No. | Make | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | ARSC | Pts |
| 1992 | Hauck Enterprises Inc. | 31 | Olds | DAY | FIF | TWS | TAL | TOL | KIL | POC | MCH | FRS | KIL | NSH | DEL | POC | HPT | FRS | ISF | TOL | DSF | TWS | SLM 22 | ATL | N/A | 0 |
| 1994 | Hauck Enterprises Inc. | 31 | Olds | DAY | TAL | FIF | LVL | KIL | TOL | FRS | MCH | DMS | POC | POC | KIL | FRS 25 | INF | I70 | ISF | DSF | TOL 19 | SLM 29 | WIN | ATL | N/A | 0 |
| 1995 | Hauck Enterprises Inc. | 31 | Olds | DAY | ATL | TAL | FIF | KIL | FRS 23 | MCH | I80 | MCS DNQ | FRS 26 | POC | POC | KIL | FRS 24 | SBS 22 | LVL | ISF | DSF | SLM 21 | WIN 26 | ATL | 49th | 620 |
| 2015 | Hauck Enterprises Inc. | 31 | Dodge | DAY | MOB | NSH | SLM | TAL | TOL 24 | NJE | POC | MCH | | WIN 14 | IOW | IRP 24 | POC | BLN 20 | ISF | DSF | SLM 26 | KEN | KAN 28 | | 32nd | 725 |
| 2015 | James Hylton Motorsports | 49 | Ford | | | | | | | | | | CHI 31 | | | | | | | | | | | | | | | | | 32nd | 725 |
| 2016 | Hauck Enterprises Inc. | 31 | Dodge | DAY | NSH | SLM 27 | TAL | TOL Wth | NJE | POC | MCH Wth | | | | | | | | | SLM 19 | CHI 27 | KEN Wth | KAN | | 23rd | 1170 |
| 2016 | Hixson Motorsports | 64 | Chevy | | | | | TOL 29 | | | | | | | | | | | | | | | | | | | | | | | | 23rd | 1170 |
| 2016 | Wayne Peterson Racing | 0 | Chevy | | | | | | | | MCH 27 | MAD 18 | WIN 20 | IOW 25 | | | | | | | | | | | | | | | 23rd | 1170 | |
| 2016 | Wayne Peterson Racing | 0 | Dodge | | | | | | | | | | | | IRP 21 | POC | BLN 18 | ISF | DSF | | | | | | | | 23rd | 1170 |
| 2017 | Hixson Motorsports | 3 | Chevy | DAY | NSH | SLM | TAL | TOL | ELK | POC | MCH | MAD | IOW | IRP | POC | WIN | ISF | ROA | DSF | SLM | CHI | KEN 29 | KAN | | 121st | 25 |
# Kevin Campbell (racing driver)

Kevin Campbell (born July 18, 1966) is an American professional stock car racing driver who has previously competed in the ARCA Menards Series.

## Racing career

In 2015, Campbell made his debut in the ARCA Racing Series at Nashville Fairgrounds Speedway, driving his own No. 81 Chevrolet, where he finished 24th due to a crash. He then made five more starts across the year, failing to finish in all of them. In 2018, he attempted to make a return to the series at the DuQuoin State Fairgrounds dirt track, but withdrew from the event.
In 2023, Campbell participated in the preseason test for the now ARCA Menards Series at Daytona International Speedway, driving the No. 82 Chevrolet for his own team, where he set the 61st and slowest time across the two sessions. He was originally scheduled to attempt to qualify for the season opening race at the track one month later with sponsorship from the University of Missouri and the Mizzou Tigers, but withdrew before practice.

## Motorsports results
### ARCA Menards Series

(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led. ** – All laps led.)
ARCA Menards Series results :
| Year | Team | No. | Make | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | AMSC | Pts |
| 2015 | KC Motorsports | 81 | Chevy | DAY | MOB | NSH 24 | SLM | TAL | TOL | NJE | POC | MCH | CHI | WIN | | IRP 33 | POC | BLN | ISF 32 | DSF 32 | SLM 33 | KEN | KAN | 60th | 395 |
| 2015 | KC Motorsports | 40 | Chevy | | | | | | | | | | | | IOW 30 | | | | | | | | | | | 60th | 395 |
| 2018 | KC Motorsports | 81 | Chevy | DAY | NSH | SLM | TAL | TOL | CLT | POC | MCH | MAD | GTW | CHI | IOW | ELK | POC | ISF | BLN | DSF Wth | SLM | IRP | KAN | N/A | 0 |
| 2023 | KC Motorsports | 82 | Chevy | DAY Wth | PHO | TAL Wth | KAN | CLT | BLN | ELK | MOH | IOW | POC | MCH | IRP | GLN | ISF | MLW | DSF | KAN | BRI | SLM | TOL | N/A | 0 |
# Kamalnayan Bajaj Hall and Art Gallery

Kamalnayan Bajaj Hall and Art Gallery is an art gallery in Mumbai, India.

## History

The art gallery, established in 1980 at Nariman Point in Mumbai in memory of philanthropist and art promoter Kamalnayan Bajaj, the elder son of Jamnalal Bajaj. The gallery showcases both emerging and established artists' work, while the hall provides a venue for social, cultural, educational, and literary events for Mumbai art circle.

## Exhibitions

* Spanda: Reverberations of the Cosmos, by Seema Lisa Pandya, January 2024.
* Ramkrishna Bajaj: A Century of Vision and Legacy, October 2023.
* Healing Through The Arts, March 2023.
* Kaliyug 3.0 by Manasa Kalyan, September 2023.
* The Future is Here, January 2019.
* Rhapsody Of Colours by Jigna Chaturvedi, April 2014.
* An Exhibition of Oil Paintings by Alka Bhandiwad, November 20-26, 2001.

## Gallery

* Inside the Kamalnayan Bajaj Hall and Art Gallery
* Subrata Sen Solo Show at Kamalnayan Bajaj Hall and Art Gallery, 2014
# Andrei Vacarciuc

Andrei Vacarciuc (born July 17, 1952) is a politician from Moldova. He has been a member of the Parliament of Moldova since 2010.
# WQLU

The Light, formerly WQLU (90.9 FM), is a non-commercial internet radio station in Lynchburg, Virginia. It broadcasts a Contemporary Christian radio format and is owned and operated by Liberty University. The station aired Liberty University Flames athletics.
WQLU was licensed for an effective radiated power (ERP) of 100 watts. The transmitter is off Candlers Mountain Road in Lynchburg. It operated from 1993 until its license was canceled in 2023. Today The Light Radio Station is solely an internet radio station.
The Light Radio station has tons of programming. They broadcast Liberty University's Convocation Service on Wednesday and Friday Mornings. They also broadcast Liberty University's Campus Community Service on Wednesday Evenings. The Light is also home to Liberty Flames Ice Hockey.

## History

Liberty University (then known as Liberty Baptist College) got its first student-run radio station in 1980, on the AM dial. It was a carrier current station available on 550 AM but only covering the campus.
On October 8, 1992, the Federal Communications Commission (FCC) granted the school a construction permit to build an FM station at 100 watts on 90.9 MHz. Its original call sign was WWMC (for "Wall to Wall Music"). The station signed on the air on February 1, 1993. During off-hours, a Christian music service from Boston was broadcast, when Liberty student DJs were not available.
After a transmitter fire, the station was off the air from June to August 1993. In 1999, the station switched from its mainstream Christian contemporary sound to a more youthful, upbeat Christian Top 40 playlist. In 2003, the station began holding on-the-air fundraisers for listener support. The station changed its call sign to WQLU in the spring of 2015.
On September 29, 2023, the FCC issued an order cancelling WQLU's license to broadcast, and requiring the university to pay a fine of $10,000, after discovering that the station had been broadcasting "from a different tower and at different geographic coordinates (...) than specified in the Station’s license." The license holder was also sanctioned for making "incorrect statements" to the FCC.
After 90.9 The Light went off of the radio airwaves, the radio station rebranded and is now The Light, where it only broadcasts over the internet as an internet radio station.
# Gorsky (surname)

Gorsky (masculine, Russian: Горский) or Gorskaya (feminine, Russian: Горская) is a Russian surname. Notable people with the surname include:
* Alex Gorsky (born 1960), American businessman, former chairman and CEO of Johnson & Johnson
* Alexander Alexeyevich Gorsky (1871–1924), Russian ballet dancer and choreographer
* Alexander Vasilyevich Gorsky (1812–1875), Russian historian
* Anatoly Gorsky (c. 1907–1980), Soviet espionage agent
* Doreen Gorsky (1912–2001), English politician
* Eugene Gorsky (1980-present), American guitarist
* Ivan Gorsky (1893–1975), Soviet geologist and paleontologist
* Vladimir Gorsky (1953-2008), Russian-American painter
* Vyacheslav Gorsky (born 1953), Russian pianist
* Yana Gorskaya (born 1977), Russian film editor
# Tyler Lewis

Tyler Lewis is an English R&B singer and songwriter of Sri Lankan, Dutch, Portuguese, and South African heritage. In 2023, Lewis became the first artist to sign to producer MNEK's MUZO by UZO record label.

## History

She appeared as a contestant in the group Nostalia on the reality television music competition Little Mix The Search, working as a receptionist at a hotel and volunteering on a farm at the time.

## Discography
### Extended plays

| Title | Details |
| Wait 'til She Gets Her Heart Broken | Released: 31 July 2024 Label: MUZO BY UZO Format: Digital download, streaming |

### Singles

| Title | Year | Album |
| "Downtime" | 2024 | Wait 'til She Gets Her Heart Broken |
| "Fly on the wall" | 2024 | Wait 'til She Gets Her Heart Broken |

### Songwriting credits

| Year | Title | Artist |
| 2023 | "Christmas All Year" | Äyanna |
| 2024 | "Boys Like U" | Äyanna |
# Biathlon at the 2017 Asian Winter Games – Mixed relay

The mixed 2×6 kilometre + 2×7.5 kilometre relay at the 2017 Asian Winter Games was held on February 25, 2017 at the Nishioka Biathlon Stadium.

## Schedule

All times are Japan Standard Time (UTC+09:00)
| Date | Time | Event |
| Saturday, 25 February 2017 | 10:00 | Final |

## Results
### Legend

* DNF — Did not finish
* DSQ — Disqualified
| Rank | Team | Penalties | Penalties | Penalties | Time |
| Rank | Team | P | S | Total | Time |
| | Kazakhstan (KAZ) | 1+5 | 0+7 | 1+12 | 1:15:40.3 |
| | Galina Vishnevskaya | 0+0 | 0+2 | 0+2 | 17:50.3 |
| | Darya Usanova | 0+2 | 0+1 | 0+3 | 18:23.9 |
| | Maxim Braun | 0+0 | 0+2 | 0+2 | 19:32.0 |
| | Yan Savitskiy | 1+3 | 0+2 | 1+5 | 19:54.1 |
| | Kazakhstan (KAZ) | 0+3 | 0+6 | 0+9 | 1:15:54.5 |
| | Alina Raikova | 0+0 | 0+1 | 0+1 | 18:04.1 |
| | Anna Kistanova | 0+2 | 0+3 | 0+5 | 19:14.3 |
| | Vassiliy Podkorytov | 0+0 | 0+1 | 0+1 | 19:03.3 |
| | Anton Pantov | 0+1 | 0+1 | 0+2 | 19:32.8 |
| | Japan (JPN) | 1+6 | 0+7 | 1+13 | 1:18:25.1 |
| | Fuyuko Tachizaki | 0+1 | 0+0 | 0+1 | 18:11.9 |
| | Yurie Tanaka | 0+2 | 0+3 | 0+5 | 20:23.5 |
| | Mikito Tachizaki | 0+0 | 0+3 | 0+3 | 19:40.2 |
| | Tsukasa Kobonoki | 1+3 | 0+1 | 1+4 | 20:09.5 |
| 4 | China (CHN) | 1+5 | 1+9 | 2+14 | 1:20:19.9 |
| | Tang Jialin | 0+0 | 0+1 | 0+1 | 18:14.8 |
| | Zhang Yan | 0+1 | 0+2 | 0+3 | 19:06.3 |
| | Tang Jinle | 1+3 | 1+3 | 2+6 | 21:45.5 |
| | Wang Wenqiang | 0+1 | 0+3 | 0+4 | 21:13.3 |
| 5 | South Korea (KOR) | 2+6 | 2+5 | 4+11 | 1:22:56.4 |
| | Mun Ji-hee | 0+0 | 0+0 | 0+0 | 18:40.1 |
| | Park Ji-ae | 0+0 | 2+3 | 2+3 | 21:01.9 |
| | Kim Yong-gyu | 0+3 | 0+1 | 0+4 | 20:38.3 |
| | Kim Jong-min | 2+3 | 0+1 | 2+4 | 22:36.1 |
| 6 | Japan (JPN) | 2+7 | 0+8 | 2+15 | 1:23:22.1 |
| | Asuka Hachisuka | 0+0 | 0+2 | 0+2 | 19:44.8 |
| | Kirari Tanaka | 2+3 | 0+2 | 2+5 | 22:26.4 |
| | Takuto Terabayashi | 0+2 | 0+2 | 0+4 | 20:15.6 |
| | Yuki Nakajima | 0+2 | 0+2 | 0+4 | 20:55.3 |
| 7 | South Korea (KOR) | 0+6 | 1+5 | 1+11 | 1:24:04.7 |
| | Jung Ju-mi | 0+0 | 0+1 | 0+1 | 19:45.9 |
| | Ko Eun-jung | 0+3 | 0+1 | 0+4 | 20:43.4 |
| | Lee In-bok | 0+0 | 0+0 | 0+0 | 21:24.3 |
| | Heo Seon-hoe | 0+3 | 1+3 | 1+6 | 22:11.1 |
| 8 | Australia (AUS) | | | | Lapped |
| | Darcie Morton | 1+3 | 0+1 | 1+4 | 22:00.4 |
| | Jillian Colebourn | 0+1 | 0+1 | 0+2 | 21:35.9 |
| | Damon Morton | 0+1 | 0+0 | 0+1 | 20:54.5 |
| | Jeremy Flanagan | | | | |
| 9 | Mongolia (MGL) | | | | Lapped |
| | Otgondavaagiin Uranbaigali | 0+0 | 1+3 | 1+3 | 23:09.7 |
| | Enkhbayaryn Ariunzul | 2+3 | 2+3 | 4+6 | 25:42.6 |
| | Battüvshingiin Bat-Erdene | 0+3 | 1+3 | 1+6 | 24:34.2 |
| | Erdenechimegiin Barkhüü | | | | |
| — | Kyrgyzstan (KGZ) | | | | DNF |
| | Kunduz Abdykadyrova | 0+2 | 3+3 | 3+5 | 28:27.9 |
| | Natalia Levdanskaia | 1+3 | 0+2 | 1+5 | 26:13.9 |
| | Nurbek Doolatov | | | | |
| | Tariel Zharkymbaev | | | | |
| — | China (CHN) | | | | DSQ |
| | Meng Fanqi | 0+1 | 0+1 | 0+2 | 19:36.2 |
| | Wu Aiting | 0+0 | 0+2 | 0+2 | 21:36.6 |
| | Hu Weiyao | 0+1 | 0+3 | 0+4 | 22:58.1 |
| | Kao Pengyu | | | | |
# North Isles (Orkney ward)

North Isles is one of the six wards used to elect members of the Orkney Islands Council. It elects three Councillors.

## Councillors

| Election | Councillors | Councillors | Councillors | Councillors | Councillors |
| 2007 | | Stephen Hagan | | Sam Harcus | Graham Sinclair |
| 2012 | Stephen Clackson | Stephen Hagan | | | Graham Sinclair |
| 2017 | Stephen Clackson | Kevin Woodbridge | | | Graham Sinclair |
| 2022 | Stephen Clackson | Heather Woodbridge | Mellissa Thomson |

## Election results
### 2022 election

North Isles - 3 seats :
| Party | Party | Candidate | FPv% | Count | Count |
| Party | Party | Candidate | FPv% | 1 | 2 |
| | Independent | Heather Woodbridge (Incumbent) | 43.1 | 443 | |
| | Independent | Stephen Clackson (incumbent) | 24.9 | 256 | 314 |
| | Independent | Mellissa Thomson | 19.8 | 204 | 268 |
| | Independent | Paul Rendall | 7.4 | 76 | 113 |
| | Independent | Sebastian Hadfield-Hyde | 4.9 | 50 | 55 |
| Electorate: 1,853 Valid: 1,029 Spoilt: 10 Quota: 258 Turnout: 56.1% ||||||
Source:

### 2017 election

2017 Orkney Islands Council election
North Isles - 3 seats :
| Party | Party | Candidate | FPv% | Count | Count | Count | Count | Count | Count | Count | Count |
| Party | Party | Candidate | FPv% | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| | Independent | Graham Sinclair (incumbent) | 26.98 | 290 | | | | | | | |
| | Independent | Kevin Woodbridge | 23.81 | 256 | 261.4 | 274.5 | | | | | |
| | Independent | Stephen Clackson (incumbent) | 18.33 | 197 | 200.6 | 207.9 | 209.0 | 219.4 | 231.5 | 247.1 | 321.9 |
| | Independent | Stuart Roy McIvor | 10.98 | 118 | 120.5 | 124.6 | 125.6 | 132.7 | 143.2 | 168.2 | |
| | Independent | Ralph Stevenson | 6.51 | 70 | 72.9 | 77.2 | 78.1 | 92.4 | 121.7 | | |
| | Independent | Simon Tarry | 6.51 | 70 | 72.8 | 72.9 | 73.5 | 78.6 | | | |
| | Independent | George Arthur Mowat-Brown | 3.35 | 39 | 39.5 | 40.6 | 41.1 | | | | |
| | Independent | Billy Muir | 3.26 | 35 | 36.1 | | | | | | |
| Electorate: 1,840 Valid: 1,075 Spoilt: 5 Quota: 269 Turnout: 1,080 (58.7%) ||||||||||||

### 2012 election

2012 Orkney Islands Council election
North Isles - 3 seats :
| Party | Party | Candidate | FPv% | Count | Count | Count | Count |
| Party | Party | Candidate | FPv% | 1 | 2 | 3 | 4 |
| | Independent | Stephen Hagan (incumbent) | 40.93 | 433 | | | |
| | Independent | Stephen Clackson | 29.1 | 308 | | | |
| | Independent | Gillian Skuse | 16.07 | 170 | 219.2 | 237.7 | |
| | Independent | Graham Sinclair (incumbent) | 13.61 | 144 | 238.1 | 249.5 | 375.1 |
| Electorate: 1,854 Valid: 1,055 Spoilt: 3 Quota: 264 Turnout: 1,058 (57.47%) ||||||||

### 2007 election

2007 Orkney Islands Council election
Orkney Islands Council election, 2007: North Isles :
| Party | Candidate | FPv% | Seat | Count |
| Independent | Stephen Hagan | 463 | 1 | 1 |
| Independent | Stephen Clackson | 154 | | |
| Independent | Sam Harcus | 133 | 2 | 7 |
| Independent | Graham Sinclair | 123 | 4 | 8 |
| Independent | Bob Trigg | 105 | | |
| Independent | William Muir | 72 | | |
| Independent | Leo Martini-Brown | 41 | | |
| Independent | George Mowat-Brown | 27 | | |
| Independent | Barbara Jeffreys | 15 | | |
# Urysohn universal space

The Urysohn universal space is a certain metric space that contains all separable metric spaces in a particularly nice manner. This mathematics concept is due to Pavel Urysohn, who presented an explicit construction. Another construction has been subsequently developed by Felix Hausdorff and a more general notion was discussed by Miroslav Katětov.

## Definition

A metric space (U,d) is called Urysohn universal if it is separable and complete and has the following property:
    given any finite metric space X, any point x in X, and any isometric embedding f : X\{x} → U, there exists an isometric embedding F : X → U that extends f, i.e. such that F(y) = f(y) for all y in X\{x}.

## Properties

If U is Urysohn universal and X is any separable metric space, then there exists an isometric embedding f:X → U. (Other spaces share this property: for instance, the space l$^∞$ of all bounded real sequences with the supremum norm admits isometric embeddings of all separable metric spaces ("Fréchet embedding"), as does the space C[0,1] of all continuous functions [0,1]→R, again with the supremum norm, a result due to Stefan Banach.)
Furthermore, every isometry between finite subsets of U extends to an isometry of U onto itself. This kind of "homogeneity" actually characterizes Urysohn universal spaces: A separable complete metric space that contains an isometric image of every separable metric space is Urysohn universal if and only if it is homogeneous in this sense.

## Existence and uniqueness

Urysohn proved that a Urysohn universal space exists, and that any two Urysohn universal spaces are isometric. This can be seen as follows. Take $(X,d),(X',d')$, two Urysohn universal spaces. These are separable, so fix in the respective spaces countable dense subsets $(x_{n})_{n},(x'_{n})_{n}$. These must be properly infinite, so by a back-and-forth argument, one can step-wise construct partial isometries $\phi _{n}:X\to X'$ whose domain (resp. range) contains $\{x_{k}:k<n\}$ (resp. $\{x'_{k}:k<n\}$). The union of these maps defines a partial isometry $\phi :X\to X'$ whose domain resp. range are dense in the respective spaces. And such maps extend (uniquely) to isometries, since a Urysohn universal space is required to be complete.
# Máriam Martínez-Bascuñán

Máriam Martínez-Bascuñán Ramírez is a Spanish political scientist. She is a professor of political science and international relations at the Autonomous University of Madrid. She specializes in feminist political theory and the study of populism. In 2018, she became the Opinion Director of the newspaper El País.

## Life and career

Martínez-Bascuñán studied law and political science at the Autonomous University of Madrid, where she received a doctorate in Political Science under the supervision of Rafael del Águila Tejerina (es). She also studied political science at Sciences Po, as well as with Iris Marion Young at The University of Chicago, and with Jean L. Cohen at Columbia University.
Martínez-Bascuñán is a Professor of Political Science and International Relations at the Autonomous University of Madrid, where she specializes in feminist political theory. She also studies the theory of gender and politics, populism, deliberative democracy, and migration policy. In 2012, she published a book about the political theory of Iris Marion Young, called Género, emancipación y diferencia(s). La teoría política de Iris Marion Young. She was also a coauthor, with Fernando Vallespín (es), of a 2017 book on populism, called Populismos.
In addition to her academic work, she has actively published opinion articles in popular media on subjects related to her academic specialties. In 2016, she became a columnist for the newspaper El País. In June 2018, she was named the Opinion Director of the newspaper.