About: Local homeomorphism

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In mathematics, more specifically topology, a local homeomorphism is a function between topological spaces that, intuitively, preserves local (though not necessarily global) structure. If is a local homeomorphism, is said to be an étale space over Local homeomorphisms are used in the study of sheaves. Typical examples of local homeomorphisms are covering maps. A topological space is locally homeomorphic to if every point of has a neighborhood that is homeomorphic to an open subset of For example, a manifold of dimension is locally homeomorphic to

Attributes	Values
rdfs:label	Homeomorfisme local (ca) Homeomorfismo local (es) Omeomorfismo locale (it) Local homeomorphism (en) 局所同相写像 (ja) Lokalny homeomorfizm (pl) Локальний гомеоморфізм (uk)
rdfs:comment	En matemàtiques, i més específicament en topologia i àrees relacionades, un homeomorfisme local és un tipus especial d'aplicació entre espais topològics, que en preserva l'estructura local. Més precisament, és una aplicació que restringida a oberts prou petits és un homeomorfisme. Els homeomorfismes locals són molt importants en geometria diferencial i en topologia algebraica, perquè són un concepte més general que inclou tant els difeomorfismes locals com els revestiments, i per la seva relació amb la . (ca) En topología, un homeomorfismo local es una aplicación de un espacio topológico en otro que respeta localmente la estructura topológica de los dos espacios. De un modo más preciso, diremos que una aplicación continua f : X → Y es un homeomorfismo local si para cada punto x de X existe un abierto U, entorno de x, tal que f(U) sea un abierto de Y y f\|U : U → f(U), la restricción de f a U sea un homeomorfismo. (es) 数学、具体的には位相幾何学において、局所同相写像 (local homeomorphism) は直感的には位相空間の間の局所的な構造を保つ関数 f である。 (ja) In topologia, un omeomorfismo locale è una funzione continua fra spazi topologici che si comporta localmente (ma non necessariamente globalmente) come un omeomorfismo. Più precisamente, una funzione continua f : X → Y è un omeomorfismo locale se ogni punto x di X ha un intorno U tale che f(U) è aperto in Y e la restrizione di f da U in f(U) è un omeomorfismo. (it) Lokalny homeomorfizm – takie przekształcenie przestrzeni topologicznych, że dla każdego istnieje takie otoczenie punktu że jest homeomorfizmem na otwarty podzbiór przestrzeni . (pl) У математиці, більш детально топології, локальний гомеоморфізм є функція між топологічними просторами що, інтуїтивно, зберігає локальну структуру. (uk) In mathematics, more specifically topology, a local homeomorphism is a function between topological spaces that, intuitively, preserves local (though not necessarily global) structure. If is a local homeomorphism, is said to be an étale space over Local homeomorphisms are used in the study of sheaves. Typical examples of local homeomorphisms are covering maps. A topological space is locally homeomorphic to if every point of has a neighborhood that is homeomorphic to an open subset of For example, a manifold of dimension is locally homeomorphic to (en)
dcterms:subject	Homeomorphisms Functions and mappings Continuous mappings General topology
Wikipage page ID	248582 (xsd:integer)
Wikipage revision ID	1122967670 (xsd:integer)
Link from a Wikipage to another Wikipage	Topological embedding Derivative Holomorphic function Homeomorphic Inclusion map Invariance of domain Inverse function theorem Complex analysis Complex plane Continuous function Mathematics Normal space Second-countable space Circle Homeomorphisms Function (mathematics) Function composition Fundamental theorem of algebra Equivalence of categories Locally compact Bijective Completely metrizable space Topology Disjoint union (topology) Domain of a function Hausdorff space Local diffeomorphism Locally compact space Locally connected space Functions and mappings Equivalence relation Fiber (mathematics) Formally étale morphism Proper map Quotient space (topology) Restriction (mathematics) Baire space Covering space Continuous mappings General topology Codomain Homeomorphism Topos Winding number Differentiable manifold Discrete space Manifold Sphere Continuous function (topology) Open map Open set Ramification (mathematics) Scheme (mathematics) Sheaf (mathematics) Étale morphism Image (mathematics) Subspace topology First-countable space Real line Topological space Universal cover Covering map Injective map Dense subset Locally injective function Locally path-connected Neighborhood (topology) Subspace (topology) dbr:Étale_geometric_morphism
sameAs	Local homeomorphism Local homeomorphism Local homeomorphism Local homeomorphism Local homeomorphism Local homeomorphism Local homeomorphism Local homeomorphism Local homeomorphism Local homeomorphism
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