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Shape morphisms and spaces of approximative maps



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Laguna, V. F. y Rodríguez Sanjurjo, José Manuel (1989) Shape morphisms and spaces of approximative maps. Fundamenta Mathematicae, 133 (3). pp. 225-235. ISSN 0016-2736

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For compact metric spaces X , Y contained in a given compact AR Q , the authors consider the set A(X,Y) of all approximative maps (in the sense of K. Borsuk [same journal 62 (1968), 223–254]). On A(X,Y) they define a metric making A(X,Y) a connected separable metric space, which contains the space of continuous mappings Y X as a closed subset. Moreover, path components of A(X,Y) coincide with homotopy classes of approximative maps. The latter property is of interest in view of the fact that these classes can be interpreted as shape morphisms from X to Y . Previously defined metrics on A(X,Y) had only the property that path connected approximative maps were homotopic, but the converse did not hold [the authors, Math. Japon. 31 (1986), no. 4, 623–633].

Tipo de documento:Artículo
Palabras clave:Shape theory; Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties); function spaces
Materias:Ciencias > Matemáticas > Geometría
Ciencias > Matemáticas > Topología
Código ID:17125
Depositado:16 Nov 2012 09:34
Última Modificación:07 Feb 2014 09:42

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