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Selections of multivalued maps and shape domination

Rodríguez Sanjurjo, José Manuel (1990) Selections of multivalued maps and shape domination. Mathematical Proceedings of the Cambridge Philosophical Society, 107 (Part 3). pp. 493-499. ISSN 0305-0041

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Abstract

Given an approximate mapping f − ={f k }:X→Y between compacta from the Hilbert cube [K. Borsuk, Fund. Math. 62 (1968), 223–254, the author associates with f − a (u.s.c.) multivalued mapping F:X→Y . If F is single-valued, F and f − induce the same shape morphism, S(F)=S(f − ) . If Y is calm [Z. Čerin, Pacific J. Math. 79 (1978), no. 1, 69–91 and all F(x) , x∈X , are sufficiently small sets, then the existence of a selection for F implies that S(f − ) is generated by some mapping X→Y . If F is associated with f − and admits a coselection (a mapping g:Y→X such that y∈F(g(y)) , for y∈Y ), then S(f − ) is a shape domination and therefore sh(Y)≤sh(X) . If Y is even an FANR, then every sufficiently small multivalued mapping F:X→Y , which admits a coselection, induces a shape domination S(F) .


Item Type:Article
Uncontrolled Keywords:Shape theory, Set-valued maps, Selections
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:17050
References:

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Deposited On:07 Nov 2012 11:21
Last Modified:07 Feb 2014 09:40

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