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has gloss | eng: In mathematics, an H-space is a topological space X (generally assumed to be connected) together with a continuous map μ : X × X → X with an identity element e so that μ(e, x) = μ(x, e) = x for all x in X. Alternatively, the maps μ(e, x) and μ(x, e) are sometimes only required to be homotopic to the identity (in this case e is called homotopy identity), sometimes through basepoint preserving maps. These three definitions are in fact equivalent for H-spaces that are CW complexes. Every topological group is an H-space; however, in the general case, as compared to a topological group, H-spaces may lack associativity and inverses. |
lexicalization | eng: H space |
lexicalization | eng: H-space |
instance of | c/Properties of topological spaces |
Meaning | |
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German | |
has gloss | deu: In der Topologie besteht ein H-Raum aus einem topologischen Raum X (oft als zusammenhängend vorausgesetzt) und einer stetigen Abbildung \mu\colon X\times X\to X mit einer Einheit e\in X in dem Sinne, dass die Endomorphismen |
lexicalization | deu: H-Raum |
Portuguese | |
has gloss | por: Em matemática, um H-espaço é um espaço topológico X (geralmente suposto conexo) juntamente com uma aplicação contínua μ : X × X → X com um elemento identidade e de modo que μ(e, x) = μ(x, e) = x para todo x em X. |
lexicalization | por: H-espaço |
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