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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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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) .

Tipo de documento:Artículo
Palabras clave:Shape theory, Set-valued maps, Selections
Materias:Ciencias > Matemáticas > Geometría
Ciencias > Matemáticas > Topología
Código ID:17050

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Depositado:07 Nov 2012 11:21
Última Modificación:07 Feb 2014 09:40

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