OpenLLM-France/wikimedia huggingface dataset:
# Lindelöf's lemma

In mathematics, Lindelöf's lemma is a simple but useful lemma in topology on the real line, named for the Finnish mathematician Ernst Leonard Lindelöf.

## Statement of the lemma

Let the real line have its standard topology. Then every open subset of the real line is a countable union of open intervals.

## Generalized Statement

Lindelöf's lemma is also known as the statement that every open cover in a second-countable space has a countable subcover (Kelley 1955:49). This means that every second-countable space is also a Lindelöf space.

## Proof of the generalized statement

Let $B$ be a countable basis of $X$. Consider an open cover, ${\mathcal {F}}=\bigcup _{\alpha }U_{\alpha }$. To get prepared for the following deduction, we define two sets for convenience, $B_{\alpha }:=\left\{\beta \in B:\beta \subset U_{\alpha }\right\}$, $B':=\bigcup _{\alpha }B_{\alpha }$.
A straight-forward but essential observation is that, $U_{\alpha }=\bigcup _{\beta \in B_{\alpha }}\beta$ which is from the definition of base. Therefore, we can get that,
${\mathcal {F}}=\bigcup _{\alpha }U_{\alpha }=\bigcup _{\alpha }\bigcup _{\beta \in B_{\alpha }}\beta =\bigcup _{\beta \in B'}\beta$
where $B'\subset B$, and is therefore at most countable. Next, by construction, for each $\beta \in B'$ there is some $\delta _{\beta }$ such that $\beta \subset U_{\delta _{\beta }}$. We can therefore write
${\mathcal {F}}=\bigcup _{\beta \in B'}U_{\delta _{\beta }}$
completing the proof.
# Lindelöf (surname)

Lindelöf is a surname of Swedish origin which may refer to:

## People

* Bernt Lindelöf, Swedish sprint canoeist who competed in the 1968 Summer Olympics
* Damon Lindelof, American television writer, executive producer and screenwriter, co-creator of the TV series Lost
* Ernst Leonard Lindelöf (1870–1946), Finnish mathematician and topologist
* Henri Lindelöf, Swedish sprint canoeist who competed in the late 1950s
* Victor Lindelöf, Swedish international footballer

## Other

* Lindelöf hypothesis, a mathematical conjecture
* Lindelöf's lemma, a mathematical terminology in topology
* Lindelöf space, a mathematical property of topological spaces
* Lindelöf's theorem, a mathematical theorem within complex analysis
* Phragmén–Lindelöf principle, a mathematical principle
* Picard–Lindelöf theorem, a mathematical theorem in the study of differential equations
* 1407 Lindelöf, a main belt asteroid with an orbital period of 1676.6949325 days
# 14th Independent Spirit Awards

The 14th Independent Spirit Awards, honoring the best in independent filmmaking for 1998, were announced on March 20, 1999. It was hosted by Queen Latifah.

## Nominees and winners

| Best Feature | Best Director |
| Gods and Monsters Affliction Claire Dolan A Soldier's Daughter Never Cries Velvet Goldmine | Wes Anderson – Rushmore Todd Haynes – Velvet Goldmine Lodge Kerrigan – Claire Dolan Paul Schrader – Affliction Todd Solondz – Happiness |
| Best Male Lead | Best Female Lead |
| Ian McKellen – Gods and Monsters Dylan Baker – Happiness Nick Nolte – Affliction Sean Penn – Hurlyburly Courtney B. Vance – Blind Faith | Ally Sheedy – High Art Katrin Cartlidge – Claire Dolan Christina Ricci – The Opposite of Sex Robin Tunney – Niagara, Niagara Alfre Woodard – Down in the Delta |
| Best Supporting Male | Best Supporting Female |
| Bill Murray – Rushmore James Coburn – Affliction Charles S. Dutton – Blind Faith Gary Farmer – Smoke Signals Philip Seymour Hoffman – Happiness | Lynn Redgrave – Gods and Monsters Stockard Channing – The Baby Dance Patricia Clarkson – High Art Lisa Kudrow – The Opposite of Sex Joely Richardson – Under Heaven |
| Best Screenplay | Best First Screenplay |
| The Opposite of Sex – Don Roos Affliction – Paul Schrader Blind Faith – Frank Military Gods and Monsters – Bill Condon The Spanish Prisoner – David Mamet | π – Darren Aronofsky High Art – Lisa Cholodenko Niagara, Niagara – Matthew Weiss Slums of Beverly Hills – Tamara Jenkins Smoke Signals – Sherman Alexie |
| Best First Feature | Best Debut Performance |
| The Opposite of Sex Buffalo '66 High Art π Slums of Beverly Hills | Evan Adams – Smoke Signals Anthony Roth Costanzo – A Soldier's Daughter Never Cries Andrea Hart – Miss Monday Sonja Sohn – Slam Saul Williams – Slam |
| Best Cinematography | Best Foreign Film |
| Velvet Goldmine – Maryse Alberti Affliction – Paul Sarossy Belly – Malik Hassan Sayeed High Art – Tami Reiker π – Matthew Libatique | The Celebration • Denmark Central Station • Brazil The Eel • Japan Fireworks • Japan The General • Ireland |

### Films that received multiple nominations

| Nominations | Film |
| 6 | Affliction |
| 5 | High Art |
| 4 | Gods and Monsters |
| 4 | The Opposite of Sex |
| 3 | Blind Faith |
| 3 | Claire Dolan |
| 3 | Happiness |
| 3 | π |
| 3 | Smoke Signals |
| 3 | Velvet Goldmine |
| 2 | A Soldier's Daughter Never Cries |
| 2 | Niagara, Niagara |
| 2 | Rushmore |
| 2 | Slam |
| 2 | Slums of Beverly Hills |

#### Films that won multiple awards

| Awards | Film |
| 3 | Gods and Monsters |
| 2 | High Art |
| 2 | The Opposite of Sex |
| 2 | Rushmore |

## Special awards
### Truer Than Fiction Award

Regret to Inform
* Dear Jesse
* Dying to Tell the Story
* Moment of Impact
* Paulina

### Producers Award

Susan A. Stover – The Sticky Fingers of Time & High Art
* Margot Bridger – Arresting Gena & The Delta
* Gill Holland – Hurricane Streets & Spring Forward
* Andrea Sperling – Nowhere & The Doom Generation

### Someone to Watch Award

David D. Williams – Thirteen
* Tony Barbieri – One
* Lynn Hershman Leeson – Conceiving Ada
* Eric Tretbar – Snow
# Senzousa

Senzousa was a town of ancient Lycaonia, inhabited in Byzantine times. The name does not occur among ancient authors but is inferred from epigraphic and other evidence.
Its site is located near Toprakkale, Asiatic Turkey.
# 14–19 Diploma

The 14-19 Diploma was a composite qualification in England launched in September 2008. Its development was announced in the 14–19 Education and Skills White Paper of March 2005. It was available to learners between the ages of 14 and 19, crossing the divide between general education and vocational education. It was closed by the Department for Education in August 2013, and is no longer offered to students.

## Diploma lines of learning, levels, and qualification structure

Diplomas were available in a range of 14 industry/employment sectors. These were known as lines of learning (rather than subjects). These include Engineering, Creative and Media and Travel and Tourism. Diplomas were not intended as preparation for direct entry into a profession, but as a general education as well as an introduction to an industry sector from which a student might progress, either through further study in full-time education, or training.
All 14 lines of learning were available at levels 1, 2 and 3 of the National Qualifications Framework. At level 1, the Diploma was known as a Foundation Diploma and was roughly equivalent in terms of challenge and volume of study to 5 GCSE qualifications at grades D - G. At level 2, the Diploma is known as a Higher Diploma which is comparable in terms of challenge and volume of study to 7 A* - C grades at GCSE. At level 3, two sizes of Diploma were available. The Advanced Diploma was comparable in challenge and volume of study to 3.5 A-levels, whereas the Progression Diploma, involved a smaller volume of study, approximated to 2.5 A-levels.
Most Diplomas had three main components: principal learning, generic learning and additional and specialist learning. Principal learning was a single qualification, based on the chosen line of learning. This qualification made up the greatest proportion of the Diploma. Generic learning included a number of sub-components: functional skills qualifications in English, Mathematics and ICT; a project qualification; a minimum of 10 days work experience and achievement of six personal, learning and thinking skills. The additional and specialist learning component permitted the student to choose to include one or more qualifications in their Diploma. These qualifications may, but do not have to, relate to the line of learning. The Progression Diploma did not include the additional and specialist learning component.

## UCAS

Although UCAS tariff points were agreed for the advanced diplomas, many universities didn't accept the qualification for entry to further study. This led to the ultimate demise of the qualification.
# Limnaecia hemidoma

Limnaecia hemidoma is a moth of the family Cosmopterigidae. It is known from Australia.
# 1561 in France

Events from the year 1561 in France

## Incumbents

* Monarch – Charles IX

## Events

* 15 May – The coronation of Charles IX
* 9 September to 9 October – The Colloquy of Poissy, a religious conference which object was to effect a reconciliation between Catholics and Protestants, took place in Poissy.

## Births

* 8 April – Dominicus Baudius, poet, scholar and historian (d. 1613)

### Full date missing

* Charles de Lorraine de Vaudémont, Roman Catholic cardinal (d. 1587)

## Deaths

* 13 February – Francis I, Duke of Nevers, commander in the French Royal Army (b. 1516)
* 15 July – Louise de Bourbon, Duchess of Montpensier, (b. 1482)
* 28 August – Jacqueline de Longwy, noblewoman, Countess of Bar-sur-Seine, Duchess of Montpensier (b. 1497).

### Full date missing

* Barthélemy Aneau, poet and humanist (b. ca 1510)
* Claude Garamond, type designer, publisher and punch-cutter (b. ca 1510)
* Claude de Longwy de Givry, bishop and Cardinal (b. 1481)
* Bernard Salomon, painter, draftsman and engraver (b. 1506)
# 1636 in poetry

Nationality words link to articles with information on the nation's poetry or literature (for instance, Irish or France).

## Works published

* Richard Brathwaite, The Fatall Nuptiall; or, Mournefull Marriage, anonymously published
* John Saltmarsh, Poemata sacra
* Wye Saltonstall, Ovids Heroicall Epistles, translated from the Latin of Ovid's Epistolae heriodum
* Longinus, On the Sublime, an edition (not in English) by Gerard Langbaine at Oxford; a widely known edition; Ancient Greek criticism; twice reprinted before 1551 (see John Hall's translation, the first into English, 1652; and Nicolas Boileau-Despréaux's influential translation into French in 1674)

## Births

Death years link to the corresponding "[year] in poetry" article:
* January 1 – Jacques Cassagne (died 1679), French clergyman, poet and moralist
* April 7 – Gregório de Matos, (died 1696), Brazilian Baroque poet
* November 1 – Nicolas Boileau-Despréaux (died 1711), French poet and critic
* Also:
** Jean de Montigny (died 1671), French poet and philosopher
** Thomas Traherne, born this year or in 1637 (died 1674), English poet and religious writer

## Deaths

Birth years link to the corresponding "[year] in poetry" article:
* January 19 – Daniel Schwenter (born 1585), German Orientalist, mathematician, inventor, poet and librarian
* August 25 – Bhai Gurdas (born 1551), Punjabi Sikh scholar, poet and scribe of the Adi Granth
# 1637 in Denmark

Events from the year 1637 in Denmark.

## Incumbents

* Monarch – Christian IV

## Events

* February – A contract was signed with a Henrik van Dingklage in Emden for the supply of bricks for the construction of Rundetårn in Copenhagen. The first three shiploads are to be delivered in May, the next three loads the following month and the remainder on demand.

### Undated

* Corfitz Ulfeldt is appointed as Governor of Copenhagen.

## Births
### Full date missing

* Dieterich Buxtehude, composer (died 1707)
* Ove Ramel, landowner (died 1685)

## Deaths

* 18 March – Dorothea Elisabeth Christiansdatter, daughter of Christian IV (born 1629)
* 9 October – Anna Svane, merchant (born c. 1573)

## Publications

* Christen Sørensen Longomontanus: Coronis Problematica ex Mysteriis trium Numerorum
# Senator Kirby (disambiguation)

William F. Kirby (1867–1934) was a U.S. Senator from Arkansas from 1916 to 1921. Senator Kirby may also refer to:
* Dean Kirby (born 1946), Mississippi State Senate
* Edward P. Kirby (1928–2017), Massachusetts State Senate
* Micajah W. Kirby (1798–1882), New York State Senate
* Moses H. Kirby (1798–1889), Ohio State Senate
# Senator Kitchen

Senator Kitchen may refer to:
* Bethuel Kitchen (1812–1895), West Virginia State Senate
* Derek Kitchen (born 1988), Utah State Senate
* Shirley Kitchen (born 1946), Pennsylvania State Senate
# Limosella australis

Limosella australis, common name Welsh mudwort, is an annual dicot plant that is indigenous to the United States and Canada. It has white flowers, and blooms between July and October. Its habitat is tidal mudflats, muddy or sandy shores It is listed as a special concern species in Connecticut.
# Sept Îles Lake (Saint-Raymond)

The Lac Sept Îles (sometimes spelled Lac aux Sept-Isles) (English: Seven Islands Lake) is a body of water located in the township of Gosford, in the municipality of Saint-Raymond, in the Portneuf Regional County Municipality, in the administrative region of Capitale-Nationale, in Quebec, in Canada.
Thanks to its forest and mountain environment, its islands and bays, its proximity to Quebec city, and the Duchesnay tourist resort, the area around the lake is highly developed. A road completely surrounds the lake to serve residents and vacationers, an activity that dates to 1857–1858, compared to 1896 at Sergent Lake.

## Geography

The Lake Sept Îles is located 6 km (3.7 mi) northeast of the village center of Saint-Raymond, in Portneuf Regional County Municipality; 2.3 km (1.4 mi) from Sergent Lake (located to the south) and 2.2 km (1.4 mi) from Saint-Joseph Lake (La Jacques-Cartier) (located to the south-east). Lake Sespt-Îles is mainly supplied by three tributaries:
* north-west: the Gosford River flowing mountains 5.7 km (3.5 mi) south-west (parallel to the Sainte-Anne River, to flow to the bottom a narrow bay which ends at the mouth of Lac des Aulnaies which is separated from Lac Sept Îles by a bridge;
* northeast: the Lac au Chien pass (0.9 km (0.56 mi) long) which links Lac au Chien (altitude of 209 m [686 ft]) and lake Sept Îles. Lac au Chien itself is fed by Lac à la Perche (217 m [712 ft]), Lac du Ventre Rouge (227 m [745 ft]), Lac des Roches, Lac Maher (241 m [791 ft]) and Lac aux Deux Truites (230 m [750 ft]);
* south-east: the outlet (about 680 m (2,230 ft) long) from Lac au Cèdre (altitude 224 m [735 ft]).
Lake Sept-Îles is surrounded by mountain peaks that reach:
* north: between 397 and 533 m (1,302 and 1,749 ft)
* south-east: between 267 and 381 m (876 and 1,250 ft)
* south: between 349 and 372 m (1,145 and 1,220 ft)
* west: 254 and 335 m (833 and 1,099 ft)
The lake has several bays including Vachon Bay (to the southeast). The mouth of the lake is located southwest of the lake. The outlet of the lake is the Portneuf River which flows southwest to the town of Portneuf where its waters flow into the St. Lawrence River.

## Toponymy

The lake is aptly named because it has exactly seven islands, three islands and four islets. Colonization around the lake began around 1857–1858; eleven families were listed there in 1861, while the population of Saint-Raymond was then 2,902 inhabitants. During the 20th century, the perimeter of the lake was fitted out with numerous houses and chalets. The island of Genois, the largest and not accessible by road, has around twenty homes. The other islands contain some habitations.
The toponym “Lac Sept Îles” was formalized on December 5, 1968, at the Bank of Place Names of the Commission de toponymie du Québec.
# Lingshou

Lingshou (灵寿) may refer to:
* Lingshou County, Hebei, China
* Lingshou Town, the seat of Lingshou County
* An Lingshou, Chinese Buddhist nun
# Lingshou Town

Lingshou (simplified Chinese: 灵寿; traditional Chinese: 靈壽; pinyin: Língshòu) is a town in and the seat of Lingshou County, in southwestern Hebei province, China, about 30 km (19 mi) north-northwest of the provincial capital of Shijiazhuang. As of 2011, it has 3 residential communities (社区) and 22 villages under its administration.
# Senator Wells

Senator Wells may refer to:

## Members of the United States Senate

* John S. Wells (1803–1860), U.S. Senator from New Hampshire in 1855
* William H. Wells (1769–1829), U.S. Senator from Delaware from 1799 to 1804 and from 1813 to 1817

## United States state senate members

* Andy Wells (American politician) (born 1954), North Carolina State Senate
* Charles Wells (American politician) (1786–1866), Massachusetts State Senate
* Erik Wells (born 1967), West Virginia State Senate
* George H. Wells (1833–1905), Louisiana State Senate
* Henry Gordon Wells (1879–1954), Massachusetts State Senate
* Henry Jackson Wells (1823–1912), Massachusetts State Senate
* Wellington Wells (1868–1954), Massachusetts State Senate
* William Wells (general) (1837–1892), Vermont State Senate
* Martin Welles (1787–1863), Connecticut State Senate

## Members of the Senate of Canada

* David Wells (politician) (born 1962), Canadian senator from Newfoundland and Labrador since 2013
# Senator Weller

Senator Weller may refer to:
* John B. Weller (1812–1875), U.S. Senator from California from 1852 to 1857
* Ovington Weller (1862–1927), U.S. Senator from Maryland from 1921 to 1927
# 1669 Dagmar

1669 Dagmar, provisional designation 1934 RS, is a rare-type Themistian asteroid from the outer region of the asteroid belt, approximately 42 kilometers in diameter. It was discovered on 7 September 1934, by German astronomer Karl Reinmuth at Heidelberg Observatory in southern Germany, and named after a common German feminine name.

## Classification and orbit

The asteroid is a member of the Themis family, a large group of asteroids in the outer main-belt. It orbits the Sun at a distance of 2.8–3.5 AU once every 5 years and 7 months (2,032 days). Its orbit has an eccentricity of 0.11 and an inclination of 1° with respect to the ecliptic. As no precoveries were taken, and no prior identifications were made, Dagmar's observation arc begins with its official discovery observation.

## Physical characteristics

Dagmar has a rare spectra of a G-type asteroid (or Cg-type in the SMASS taxonomy), similar to 1 Ceres, the largest asteroid and only dwarf planet in the asteroid belt.

### Rotation period

Astronomer Federico Manzini obtained a provisional lightcurve of Dagmar from photometric observations in March 2004. It gave a tentative rotation period of 12 hours with a brightness variation of 0.15 magnitude (U=1). As of 2017, no secure period has yet been published.

### Diameter and albedo

According to the surveys carried out by the Infrared Astronomical Satellite IRAS, the Japanese Akari satellite, and NASA's Wide-field Infrared Survey Explorer with its subsequent NEOWISE mission, Dagmar measures between 35.78 and 45.194 kilometers in diameter, and its surface has an albedo between 0.035 and 0.057. The Collaborative Asteroid Lightcurve Link adopts the results obtained by 17 observations made by IRAS, that is an albedo of 0.0565 and a diameter of 35.78 kilometers with an absolute magnitude of 10.97.

## Naming

This minor planet was named by the discoverer after a common German feminine name. No special meaning is assigned to this name. The official naming citation was published by the Minor Planet Center on 15 December 1968 (M.P.C. 2901).
# 163 (disambiguation)

163 may refer to:

## Dates

* 163 CE, a common year of the Julian calendar
* 163 BC, a year of the pre-Julian Roman calendar

## Number

* 163 (number), the natural number following 162 and preceding 164

## Other

* 163 (New Jersey bus)
* Messerschmitt Me 163
* U.S. Route 163, a 64-mile (103 km) U.S highway
* California State Route 163, a state highway in San Diego, California
* Virginia State Route 163, a primary state highway in the U.S. state of Virginia
* Washington State Route 163, a state highway in Washington state
* 163.com or NetEase
* Tatra 163, a heavy truck
# 1639 in science

The year 1639 in science and technology involved some significant events.

## Astronomy

* Giovanni Battista Zupi observes that the planet Mercury has orbital phases.
* December 4 (November 24 in Julian calendar) – English astronomers Jeremiah Horrocks and William Crabtree are the first and only scientific observers of a transit of Venus, predicted by Horrocks.

## Exploration

* The Casiquiare canal, a river forming a natural canal between the Amazon River and Orinoco River basins, is first encountered by Europeans

## Mathematics

* Girard Desargues introduces the concept of infinity into geometry.

## Births

* April 12 – Martin Lister, English naturalist and physician (died 1712)
* December 18 – Gottfried Kirch, German astronomer (died 1710)
* approx. date – Daniel Greysolon, Sieur du Lhut, French explorer (died 1710)

## Deaths

* June 6 – Peter Crüger, German polymath (born 1580)
* August 7 – Martin van den Hove, Dutch astronomer (born 1605)
* Mutio Oddi, Italian mathematician (born 1569)
# 1801 in Chile

The following lists events that happened during 1801 in Chile.

## Incumbents

Royal Governors - Joaquín del Pino (-March 31), José de Santiago Concha Jiménez Lobatón (April 1-December), Francisco Tadeo Diez de Medina Vidanges (December-)

## Births

May 6 - José Joaquín Pérez, seventh president of Chile. (d. 1889)
# Lissoglossa

Lissoglossa is a genus of flies in the family Tachinidae.

## Species

* Lissoglossa bequaerti Villeneuve, 1912
* Lissoglossa taeniata Villeneuve, 1912