OpenLLM-France/wikimedia huggingface dataset:
# Caristi fixed-point theorem

In mathematics, the Caristi fixed-point theorem (also known as the Caristi–Kirk fixed-point theorem) generalizes the Banach fixed-point theorem for maps of a complete metric space into itself. Caristi's fixed-point theorem modifies the $\varepsilon$-variational principle of Ekeland (1974, 1979). The conclusion of Caristi's theorem is equivalent to metric completeness, as proved by Weston (1977). The original result is due to the mathematicians James Caristi and William Arthur Kirk.
Caristi fixed-point theorem can be applied to derive other classical fixed-point results, and also to prove the existence of bounded solutions of a functional equation.

## Statement of the theorem

Let $(X,d)$ be a complete metric space. Let $T:X\to X$ and $f:X\to [0,+\infty )$ be a lower semicontinuous function from $X$ into the non-negative real numbers. Suppose that, for all points $x$ in $X,$ $d(x,T(x))\leq f(x)-f(T(x)).$
Then $T$ has a fixed point in $X;$ that is, a point $x_{0}$ such that $T(x_{0})=x_{0}.$ The proof of this result utilizes Zorn's lemma to guarantee the existence of a minimal element which turns out to be a desired fixed point.
# Karatin al-Kabir

Karatin al-Kabir (Arabic: كراتين الكبير) is a Syrian village located in Sinjar Nahiyah in Maarrat al-Nu'man District, Idlib. According to the Syria Central Bureau of Statistics (CBS), Karatin al-Kabir had a population of 93 in the 2004 census.
# Tom Crouch (footballer)

Tom Crouch (23 February 1916 – 27 September 1990) was a former Australian rules footballer who played with Footscray in the Victorian Football League (VFL).
# Reefton Spicer

Reefton Harry Adolphus Spicer (17 July 1898 – 22 April 1978) was an Australian rules footballer who played with Richmond in the Victorian Football League (VFL).

## Family

The son of Ernest Edward Spicer (1877-1936), and Adelina Ann Elizabeth Spicer (1877-1943), née Bailhache, Reefton Harry Adolphus Spicer, known as "Harry", was born at South Yarra, Victoria on 17 July 1898.
He married Doris Annie O'Brien (1900-1974) in 1925.

## Football
### Richmond (VFL)

Recruited from Richmond Districts, he played on the wing and in the back-pocket for the Richmond Football Club — in one senior game in 1917, and in two senior games in 1918.

### Brunswick (VFA)

Cleared from Richmond, he played one senior game for the Brunswick Football Club in 1919.

### Williamstown (VFA)

He played four senior games for the Williamstown Football Club in 1920.

## Death

He died at Brighton, Victoria on 22 April 1978.

## Footnotes

* ↑ Holmesby & Main (2014), p.839.
* ↑ Deaths: Spicer, The Age, (Tuesday, 11 August 1936), p.1.
* ↑ Marriages: Spicer—Bailhache, The Age(Saturday, 26 November 1898), p.5: married at South Yarra on 31 August 1897.
* ↑ Deaths: Spicer, The Argus, (Thursday, 3 June 1943), p.2.
* ↑ He was named "Reefton" after his father's birthplace: his father was born at Reefton, in New Zealand, in 1877.
* ↑ Hogan (1996), p.215.
* ↑ Football, The Age, (Friday, 2 May 1919), p.9.
* ↑ Deaths: "Spicer, Harry", The Age, (Monday, 24 April 1978), p.22.
# Willem Gerrit Dedel (1726–1768)

Willem Gerrit Dedel (17 May 1726 in The Hague – 26 January 1768 in Büyükelçi (Constantinople)) was a Dutch politician and diplomat, who represented the States General of the Dutch Republic at the Sublime Porte.

## Personal life

Dedel was the son of Jan Hudde Dedel, burgemeester of The Hague, and Magdalena Antonia Muyssart. He never married.

## Career

Dedel was Postmaster of the Post Office for Brabant, France, Spain and Portugal in The Hague before 1742. In 1758 he was appointed a Commissioner of Amsterdam and captain of the Amsterdam schutterij. Promoted to Colonel in 1764. In 1763 he was elected schepen of Amsterdam.
In 1764 he was appointed ambassador of the States General at the court of the Sultan of the Ottoman Empire, Mustafa III, as successor of ambassador Mathias van Asten, who died in 1764 in office. It took him until the next year, however, before he undertook the voyage together with two companions: Johan Raye van Breukelerwaard and Jan Abraham Meijn van Spanbroek. He wrote a journal about the journey, entitled: Kort dagverhael van mijn rijze uyt den Haeg nae Constantinopel welke ik begonnen heb in het einde van het jaer 1764 (Short journal of my voyage from the Hague to Constantinople that I started on at the end of the year 1764).
After his arrival in 1765 he spent three years at the Porte. He died in office in his mansion in the diplomatic quarter of Constantinople in 1768
# Rianne Sigmond

Rianne Sigmond (born 2 May 1984) is a Dutch rower. She competed in the women's lightweight double sculls event at the 2012 Summer Olympics.
# Greg Burgess (footballer)

Greg Burgess (born 8 August 1945) is a former Australian rules footballer who played with Hawthorn in the Victorian Football League (VFL).
# Tommy McCarthy (ice hockey)

Thomas Edward McCarthy (April 12, 1893 – December 28, 1959) was a professional ice hockey player who played two seasons in the National Hockey League for the Quebec Bulldogs and Hamilton Tigers. After several years as an amateur player with teams in New York, McCarthy joined the amateur Hamilton Tigers in 1918–19 and helped them win the Allan Cup as the best amateur team in Canada. He turned professional in 1919 when he joined the Bulldogs and played one season with the team before they moved and became the professional Tigers. McCarthy played an additional season there before joining the Saskatoon/Moose Jaw Crescents of the Western Canada Hockey League, and played one final season with the Seattle Metropolitans of the Pacific Coast Hockey Association before retiring in 1923.

## Playing career

He played one season for the Quebec Bulldogs (1919–20) and one for the Hamilton Tigers (1920–21) of the NHL and one season for the Seattle Metropolitans (1922–23) of the PCHA. In 35 NHL games, he scored 22 goals and added 7 assists for 29 points. In 16 PCHA games, he scored two goals and one assist.

## Career statistics
### Regular season and playoffs

| | | | Regular season | Regular season | Regular season | Regular season | Regular season | Playoffs | Playoffs | Playoffs | Playoffs | Playoffs |
| Season | Team | League | GP | G | A | Pts | PIM | GP | G | A | Pts | PIM |
| 1914–15 | New York Irish-Americans | AAHL | 8 | 5 | 0 | 5 | — | — | — | — | — | — |
| 1915–16 | Brooklyn Crescents | AAHL | 7 | 5 | 0 | 5 | — | — | — | — | — | — |
| 1916–17 | Brooklyn Crescents | AAHL | 12 | 14 | 0 | 14 | — | — | — | — | — | — |
| 1917–18 | New York Wanderers | USNHL | 10 | 4 | 0 | 4 | — | — | — | — | — | — |
| 1918–19 | Hamilton Tigers | OHA | 8 | 19 | 3 | 22 | — | 4 | 3 | 2 | 5 | — |
| 1918–19 | Hamilton Tigers | Al-Cup | — | — | — | — | — | 2 | 1 | 0 | 1 | 0 |
| 1919–20 | Quebec Bulldogs | NHL | 12 | 12 | 6 | 18 | 0 | — | — | — | — | — |
| 1920–21 | Hamilton Tigers | NHL | 23 | 10 | 1 | 11 | 10 | — | — | — | — | — |
| 1921–22 | Saskatoon/Moose Jaw Crescents | WCHL | 7 | 1 | 0 | 1 | 0 | — | — | — | — | — |
| 1922–23 | Seattle Metropolitans | PCHA | 16 | 2 | 1 | 3 | 0 | — | — | — | — | — |
| NHL totals | NHL totals | NHL totals | 35 | 22 | 7 | 29 | 10 | — | — | — | — | — |
# John Plumridge

John Kevin Plumridge (born 13 April 1944 – 28 June 2016) was an Australian rules footballer who played with South Melbourne in the Victorian Football League (VFL).
# Camilla Forcinella

Camilla Forcinella (born 22 January 2001) is an Italian professional footballer who plays as goalkeeper for Serie B club Genoa CFC on loan from Juventus. She has also represented her country in youth level.

## Career
### Club

Camilla Forcinella made her senior debut for AGSM Verona in the Serie A at the age of 16. After Verona was acquired by Hellas Verona FC in 2018, she became the first-choice goalkeeper, making 37 total appearances and conceding 83 goals in the following two seasons.
On 29 July 2020, she joined Fiorentina. In the 2020/21 season, she only made 3 appearances and, on 12 January 2022, she joined Juventus on loan. After they won the 2021/22 Serie A, she joined Juventus permanently, making her debut on 5 January 2023 in a Coppa Italia match against Cittadella. On 19 July 2023, she joined Serie B club Genoa on loan until the end of the 2023/24 season.

### International

Forcinella made her debut for the Italian U17 team against Portugal on 28 October 2016 at the 2017 UEFA Women's Under-17 Championship qualification. She also competed in the 2018 edition as well as the 2018 UEFA Women's Under-17 Championship. In total, she made 7 appearances and kept 3 clean sheets.
She made her debut for the Italian U19 team in a 4–0 win over Romania on 4 October 2018 at the 2019 UEFA Women's Under-19 Championship qualification. She also competed in the 2020 edition.

## Honours
### Juventus

* Serie A (1): 2021/22
* Coppa Italia (2): 2021/22, 2022/23
# Miroslava, Iași

Miroslava is a commune in Iași County, Western Moldavia, Romania, part of the Iași metropolitan area. It is composed of thirteen villages: Balciu, Brătuleni, Ciurbești, Cornești, Dancaș, Găureni, Horpaz, Miroslava, Proselnici, Uricani, Valea Adâncă, Valea Ursului, and Vorovești.
The commune is situated in the Jijia Plain, at an altitude of 133 m (436 ft), on the banks of the river Valea Locii. It is located in the central part of the county, 7 km (4.3 mi) west of the county seat, Iași, on county road DJ248A.

## Uricani transmitter

At Uricani, there is a mediumwave transmitter, which transmits on 1053 kHz with a power of 1000 kW. It is one of the most powerful transmitters in Romania and uses two guyed masts insulated against ground with a height of 165 metres as antenna.

## Sport

The football club CS Știința Miroslava is based in the commune. Its home ground is the Comunal Stadium in Uricani.

## Natives

* Dimitrie Anghel (1872–1914), poet
# Rock tripe

Rock tripe is the common name for various lichens of the genus Umbilicaria that grow on rocks. They are widely distributed, including on bare rock in Antarctica, and throughout northern parts of North America such as New England and the Rocky Mountains. They are edible when properly prepared; soaking extensively and boiling with changes of water removes the bitterness and purgative properties. They have been used as a famine food in extreme cases when other food sources were unavailable, as by early American northern explorers.
Umbilicaria esculenta is commonly used as a food in Asian cuisine and a restorative medicine in traditional Chinese medicine.

## Species

* Umbilicaria ahtii Davydov (2024)
* Umbilicaria americana Poelt & T.H.Nash (1993)
* Umbilicaria angulata Tuck. (1848)
* Umbilicaria antarctica Frey & I.M.Lamb (1939)
* Umbilicaria aprina Nyl. (1869)
* Umbilicaria arctica (Ach.) Nyl. (1859)
* Umbilicaria bigleri Frey (1949)
* Umbilicaria crustulosa (Ach.) Lamy (1879)
* Umbilicaria cylindrica (L.) Delise (1830)
* Umbilicaria daliensis (J.C.Wei) Davydov, Peršoh & Rambold (2018)
* Umbilicaria decussata (Vill.) Zahlbr. (1932)
* Umbilicaria deusta (L.) Baumg. (1790)
* Umbilicaria dura McCune (2018) – North America
* Umbilicaria esculenta (Miyoshi) Minks (1900)
* Umbilicaria hirsuta (Sw. ex Westr.) Ach. (1794)
* Umbilicaria hispanica (Frey) Davydov, Peršoh & Rambold (2018)
* Umbilicaria hyperborea (Ach.) Hoffm. (1796)
* Umbilicaria iberica Sancho & Krzew. (2009)
* Umbilicaria isidiosa Krzew. (2009)
* Umbilicaria leiocarpa DC. (1805)
* Umbilicaria maculata Krzew., M.P.Martín & M.A.García (2009)
* Umbilicaria mammulata (Ach.) Tuck. (1848)
* Umbilicaria meizospora (Harm.) E.A.Davydov & D.Masson (2022) – Europe
* Umbilicaria muhlenbergii (Ach.) Tuck. (1845)
* Umbilicaria multistrata McCune (2018) – North America
* Umbilicaria murihikuana D.J.Galloway & Sancho (2005)
* Umbilicaria nodulospora McCune, Di Meglio & M.J.Curtis (2014)
* Umbilicaria nylanderiana (Zahlbr.) H.Magn. (1937)
* Umbilicaria orientalis Davydov (2020) – East Asia
* Umbilicaria phaea Tuck. (1869)
* Umbilicaria platyrhiza Davydov (2022)
* Umbilicaria polyphylla (L.) Baumg. (1790)
* Umbilicaria polyrrhiza (L.) Fr. (1825)
* Umbilicaria proboscidea (L.) Schrad. (1794)
* Umbilicaria propagulifera (Vain.) Lano (1950)
* Umbilicaria pulvinaria (Savicz) Frey (1931)
* Umbilicaria rhizinata (Frey & Poelt) Krzew. (2010)
* Umbilicaria rigida (Du Rietz) Frey (1931)
* Umbilicaria robusta (Llano) D.J.Galloway & Sancho (2005)
* Umbilicaria sinorientalis (J.C.Wei) Davydov, Peršoh & Rambold (2018)
* Umbilicaria spodochroa Ehrh. ex Hoffm. (1796)
* Umbilicaria subglabra (Nyl.) Harm. (1910)
* Umbilicaria torrefacta (Lightf.) Schrad. (1794)
* Umbilicaria vellea (L.) Ach. (1794)
* Umbilicaria virginis Schaer. (1842)
* Umbilicaria xizangensis (J.C.Wei & Y.M.Jiang) Davydov, Peršoh & Rambold (2018)

## Gallery

* Rock Tripe (seogi) with pine nuts
* Lichens of the type eaten by John Franklin's men on their journey back from the Coppermine River
* Kishū kumano iwatake tori ("Iwatake mushroom gathering at Kumano in Kishu") by Hiroshige II
* Umbilicaria havaasii
# Songdo (disambiguation)

Songdo (Korean: 송도, alternatively from 松都, "Pine City", or 松島, "Pine Island(s)"), may refer to:
* Kaesong, North Korea
* Songdo Point, North Korea
* Songdo International Business District, a district in Incheon, South Korea
* Songdo Beach in Busan, South Korea
# Pat Dooley (footballer)

Patrick Dooley (20 October 1898 – 3 April 1969) was an Australian rules footballer who played with Richmond in the Victorian Football League (VFL).
# Gruppo

Gruppo may refer to:
* Gruppo (music), a type of cadential trill in music
* groupset, a bicycle component manufacturer's organized collection of mechanical parts
* Leonard Gruppo (born 1942), a politician in Pennsylvania
# Ron Workman

Ron Workman (born 7 June 1939) is an Australian former professional rugby league footballer who played in the 1960s and 1970s. He played for Parramatta and Penrith as a hooker. Workman was a foundation player for Penrith and played in the club's first ever game.

## Early life

Workman was born in Sydenham in the inner suburbs of Sydney and grew up there. In 1954, at the age of 15, he began an apprenticeship with the Royal Australian Air Force, and he later became a serving member.

## Playing career

Workman made his first grade debut for Parramatta in 1961 and played 4 seasons at the club but mainly featured for the lower grade sides only managing to make a total of 10 first grade appearances. Workman then went and served for the Australian Air Force in the Vietnam War before returning to Australia in 1966. In 1967, Workman joined newly admitted side Penrith and played in the club's first ever game against Canterbury. Workman played 6 seasons for Penrith and was named captain of the side in 1970. At the end of 1973, Workman left Penrith and moved to North Queensland playing in the local competition there before retiring.

## Post playing

After retiring from rugby league, Workman became club secretary of Penrith in 1975 and later became one of the club's administrators.
# Norm Gordes

Norm Gordes (born 8 January 1946) is a former Australian rules footballer who played with Hawthorn in the Victorian Football League (VFL).
# Peter McCracken (footballer, born 1949)

Peter McCracken (born 1 December 1949) is a former Australian rules footballer who played for the South Melbourne Football Club in the Victorian Football League (VFL).
# Acer binzayedii

Acer binzayedii, commonly known as algodoncillo, is a species of flowering plant in the genus Acer. It is endemic to Jalisco State in western Mexico. It has a limited range, and is considered Critically Endangered.

## Description

Acer binzayedii is a large tree, growing to between 20 and 30 meters in height. It flowers between December and January and sets fruit from March.

## Taxonomy

The formal description of the species reads as follows: "The specific epithet honours a philanthropist committed to the protection of the environment and the preservation of species, His Highness Sheikh Mohammed bin Zayed Al Nahyan, Crown Prince of Abu Dhabi and Deputy Supreme Commander of the United Arab Emirates Armed Forces. Through his philanthropic endowment, the first author was able to conduct phylogeographic and taxonomic studies of Acer in tropical America; this research led to the discovery and recognition of this new species."
Until 2017 it was considered a western population of Acer skutchii.

## Range and habitat

Acer binzayedii is native to ravine montane cloud forests in the Sierra de Manantlán of western Jalisco State. It known from two remnant populations, each less than two hectares in area, between 1,790 and 1,880 meters elevation. Mean temperature is 18.5 °C. The two cloud forest remnants are separated by pine–oak forest.
It grows on intermediate rocks and cambisol soil. It is typically found in association with Carpinus tropicalis, Cornus disciflora, Dendropanax arboreus, Ostrya virginiana, and Quercus salicifolia. A. binzayedii is susceptible to fire.

## Conservation

Human disturbance is causing species' habitat to decline in area, extent and quality. The species also suffers from low genetic diversity.
The population was formerly larger, but only 90 mature trees have been observed, along with a larger number of young trees.
# Pestalotiopsis microspora

Pestalotiopsis microspora is a species of endophytic fungus capable of breaking down and digesting polyurethane. Originally identified in 1880 in fallen foliage of common ivy (Hedera helix) in Buenos Aires, it also causes leaf spot in Hypericum 'Hidcote' (Hypericum patulum) shrubs in Japan.
However, its polyurethane degradation activity was discovered only in the 2010s in two distinct P. microspora strains isolated from plant stems in the Yasuni National Forest within the Ecuadorian Amazon rainforest by a group of student researchers led by molecular biochemistry professor Scott Strobel as part of Yale's annual Rainforest Expedition and Laboratory. It is the first fungus species found to be able to subsist on polyurethane in anaerobic conditions. This makes the fungus a potential candidate for bioremediation projects involving large quantities of plastic.
Pestalotiopsis microspora was originally described from Buenos Aires, Argentina in 1880 by mycologist Carlo Luigi Spegazzini, who named it Pestalotia microspora.
In 1996 Julie C. Lee first isolated Torreyanic acid, a dimeric quinone, from P. microspora, and noted that the species is likely the cause of the decline of Florida torreya (Torreya taxifolia), an endangered species of a tree that is related to the paclitaxel-producing yew tree Taxus brevifolia.
Pestalotiopsis microspora is a fungus that is known to be the most effective when it comes to penetrating the exterior of a polymer product or polyurethane and dissolving it through the oxidizing enzymes that it possesses. Although this is an amazing discovery, it has mostly been monitored in laboratory settings and still needs more experimentation to use on a wide scale for landfills and clean-up areas.
# Karsanti

Karsanti (Arabic: كرسنتي) is a Syrian village located in Sinjar Nahiyah in Maarrat al-Nu'man District, Idlib. According to the Syria Central Bureau of Statistics (CBS), Karsanti had a population of 219 in the 2004 census.
# Billy Stephens

Billy Stephens (28 July 1918 – 16 September 2006) was a former Australian rules footballer who played with Footscray in the Victorian Football League (VFL).
# Artie Fewster

Arthur Leslie Fewster (18 October 1894 – 13 January 1960) was an Australian rules footballer who played for the Richmond Football Club in the Victorian Football League (VFL).
# Johnny Slade

John 'Johnny' Slade (1933–1991) was an Australian rugby league footballer who played in the 1950s.

## Playing career

Originally from the Stockton, New South Wales area, Slade was a fullback for the Parramatta Eels between 1953 and 1955, then in 1958 and 1959.
He is remembered for his long range kicking, especially his kicking duels with rival fullbacks and was a crowd favourite at Cumberland Oval. Slade played 77 games with Parramatta in his career, scoring 16 tries, 36 goals and two field goals for a total of 124 points. He also holds the record as the youngest first grade captain-coach when he coached the blue and golds in 1955 at age 21, being the last coach of the club to avoid the wooden spoon until Ken Kearney seven seasons later.
He returned to Newcastle at the end of his playing career.

## Death

Slade died on 4 February 1991, aged 57.
# John Price (Australian footballer)

John Price (born 24 September 1944) is a former Australian rules footballer who played with Hawthorn in the Victorian Football League (VFL).
# Jeff Fehring

Jeff Fehring (21 April 1955 – 25 July 2008) was an Australian rules footballer who played for Geelong and St Kilda in the Victorian Football League (as the AFL was then known) from 1977 to 1981.
Fehring was born at Leitchville, on the Murray River, near Echuca. He made his debut as a ruckman with the Geelong Football Club in 1977, playing 19 games and kicking 1 goal until 1979. He moved to St Kilda in 1980, and in 1981 his moment of fame came. While he only went on to play 17 games and kick 3 goals for St Kilda, one of those goals was a huge torpedo punt that was estimated to be 84–86 metres, kicked from beyond the centre circle at Moorabbin in 1981. The goal came minutes after he was reported, and he was so fired up that he kicked the (wind-assisted) goal, one of the biggest in Australian rules football history.
Fehring's VFL career was over at the end of the 1981 season, and he moved to Adelaide to play for Norwood Football Club in the South Australian National Football League (SANFL). After playing in Norwood's 1982 premiership, Fehring retired from football and became a cattle farmer after marrying in 1984, but with water prices affected by drought, he was forced to sell his farm and livestock and move to Alexandra, where it was hoped there would be more rain. Despite working several jobs, Fehring lost his emu and cattle farm, and his marriage. Taking custody of his two children, he moved to Darwin briefly, before buying a pub and hotel in Deniliquin in southern New South Wales. That business also failed, and beset by health problems including Type 2 diabetes and recurring heart problems, Fehring committed suicide on 25 July 2008.
# Camillo Girotti

Camillo Girotti (born 27 February 1918) was an Italian professional football player.

## Honours

* Coppa Italia winner: 1938/39.
* This biographical article related to association football in Italy, about a defender born in the 1910s, is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
# Harvey Bennett Sr.

Harvey Alexander Bennett Sr. (July 23, 1925 – November 21, 2004) was a Canadian professional ice hockey goaltender who played for the Boston Bruins of the National Hockey League.
Perhaps Bennett's most famous feat was surrendering Maurice Richard's goal that established scoring 50 goals in 50 games. This goal was scored for the Bruins' nemesis Montreal Canadiens on March 18, 1945.
Bennett was inducted into the American Hockey League Hall of Fame in 2013 and the Rhode Island Hockey Hall of Fame in 2018.

## Family

He was born in Ettington, Saskatchewan and married Diana Helen Sullivan (youngest of nine sisters). Of his six sons, Harvey Bennett Jr., Curt Bennett, and Bill Bennett all played in the NHL. John Bennett played in the WHA, and Jimmy Bennett was a 1977 draft pick of the Atlanta Flames who played professionally in the International Hockey League with the Muskegon Mohawks and also in the old Central Hockey League with the Birmingham Bulls. His youngest son, Peter Bennett, drowned after falling through ice.