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Shape morphisms and spaces of approximative maps

Laguna, V. F. and 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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Abstract

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].


Item Type:Article
Uncontrolled Keywords:Shape theory; Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties); function spaces
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:17125
Deposited On:16 Nov 2012 09:34
Last Modified:07 Feb 2014 09:42

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