First-countable space (original) (raw)
En Topologia, un espai topològic compleix el primer axioma de numerabilitat si cada punt de l'espai té una numerable. Si un espai compleix aquest axioma, es diu que és primer contable o primer numerable.
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| dbo:abstract | En Topologia, un espai topològic compleix el primer axioma de numerabilitat si cada punt de l'espai té una numerable. Si un espai compleix aquest axioma, es diu que és primer contable o primer numerable. (ca) In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability". Specifically, a space is said to be first-countable if each point has a countable neighbourhood basis (local base). That is, for each point in there exists a sequence of neighbourhoods of such that for any neighbourhood of there exists an integer with contained in Since every neighborhood of any point contains an open neighborhood of that point, the neighbourhood basis can be chosen without loss of generality to consist of open neighborhoods. (en) En Topología, se dice que un espacio topológico cumple el primer axioma de numerabilidad si cada punto del espacio tiene una base de entornos numerable. Si un espacio cumple este axioma se dice que es primero contable o primero numerable. (es) En mathématiques, un espace topologique X est à bases dénombrables de voisinages si tout point x de X possède une base de voisinages dénombrable, c'est-à-dire s'il existe une suite V0, V1, V2, … de voisinages de x telle que tout voisinage de x contienne l'un des Vn. Cette notion a été introduite en 1914 par Felix Hausdorff. (fr) In topologia, uno spazio topologico si dice primo-numerabile se soddisfa il primo assioma di numerabilità, ovvero se ogni suo punto ammette un sistema fondamentale di intorni numerabile. (it) 일반위상수학에서 제1 가산 공간(第一可算空間, 영어: first-countable space)은 모든 점이 가산 국소 기저를 갖는 위상 공간이다. 제1 가산 공간에서는 일반적으로 그물 또는 필터를 사용하여 정의되는 조건들이 점렬을 사용한 조건들과 동치가 된다. (ko) 数学の位相空間論において、第一可算空間（だいいちかさんくうかん、英: first-countable space）とは、"第一可算公理"を満たす位相空間のこと。位相空間 X が第一可算公理を満たすとは「各点 x が高々可算な近傍からなる基本近傍系（局所基）をもつこと」を指す。すなわちx の可算個の開近傍 U1, U2, …で以下の性質を満たすものが存在するということである：x の任意の近傍 V に対しある が存在し、Vは Uiを部分集合として含む。 (ja) Первая аксиома счётности ― понятие общей топологии.Топологическое пространство удовлетворяет первой аксиоме счётности, если всякой его точки обладает счётной базой. (ru) 在拓撲學上，第一可數空間（First-countable space）是指有可數的邻域基的拓撲空間，即對於，存在的開鄰域序列，使得對於任意的鄰域，存在整數使得。 (zh) Перша аксіома зліченності — властивість деяких топологічних просторів. (uk) |
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| dbp:title | first axiom of countability (en) |
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| rdfs:comment | En Topologia, un espai topològic compleix el primer axioma de numerabilitat si cada punt de l'espai té una numerable. Si un espai compleix aquest axioma, es diu que és primer contable o primer numerable. (ca) In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability". Specifically, a space is said to be first-countable if each point has a countable neighbourhood basis (local base). That is, for each point in there exists a sequence of neighbourhoods of such that for any neighbourhood of there exists an integer with contained in Since every neighborhood of any point contains an open neighborhood of that point, the neighbourhood basis can be chosen without loss of generality to consist of open neighborhoods. (en) En Topología, se dice que un espacio topológico cumple el primer axioma de numerabilidad si cada punto del espacio tiene una base de entornos numerable. Si un espacio cumple este axioma se dice que es primero contable o primero numerable. (es) En mathématiques, un espace topologique X est à bases dénombrables de voisinages si tout point x de X possède une base de voisinages dénombrable, c'est-à-dire s'il existe une suite V0, V1, V2, … de voisinages de x telle que tout voisinage de x contienne l'un des Vn. Cette notion a été introduite en 1914 par Felix Hausdorff. (fr) In topologia, uno spazio topologico si dice primo-numerabile se soddisfa il primo assioma di numerabilità, ovvero se ogni suo punto ammette un sistema fondamentale di intorni numerabile. (it) 일반위상수학에서 제1 가산 공간(第一可算空間, 영어: first-countable space)은 모든 점이 가산 국소 기저를 갖는 위상 공간이다. 제1 가산 공간에서는 일반적으로 그물 또는 필터를 사용하여 정의되는 조건들이 점렬을 사용한 조건들과 동치가 된다. (ko) 数学の位相空間論において、第一可算空間（だいいちかさんくうかん、英: first-countable space）とは、"第一可算公理"を満たす位相空間のこと。位相空間 X が第一可算公理を満たすとは「各点 x が高々可算な近傍からなる基本近傍系（局所基）をもつこと」を指す。すなわちx の可算個の開近傍 U1, U2, …で以下の性質を満たすものが存在するということである：x の任意の近傍 V に対しある が存在し、Vは Uiを部分集合として含む。 (ja) Первая аксиома счётности ― понятие общей топологии.Топологическое пространство удовлетворяет первой аксиоме счётности, если всякой его точки обладает счётной базой. (ru) 在拓撲學上，第一可數空間（First-countable space）是指有可數的邻域基的拓撲空間，即對於，存在的開鄰域序列，使得對於任意的鄰域，存在整數使得。 (zh) Перша аксіома зліченності — властивість деяких топологічних просторів. (uk) |
| rdfs:label | Primer axioma de numerabilitat (ca) Primer axioma de numerabilidad (es) First-countable space (en) Spazio primo-numerabile (it) Espace à bases dénombrables de voisinages (fr) 第一可算的空間 (ja) 제1 가산 공간 (ko) Первая аксиома счётности (ru) Перша аксіома зліченності (uk) 第一可數空間 (zh) |
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