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Approximation by light maps and parametric Lelek maps
Authors:Taras Banakh  Vesko Valov
Institution:a Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Ukraine
b Instytut Matematyki, Akademia ?wi?tokrzyska w Kielcach, Poland
c Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada
Abstract:The class of metrizable spaces M with the following approximation property is introduced and investigated: MAP(n,0) if for every ε>0 and a map g:InM there exists a 0-dimensional map g:InM which is ε-homotopic to g. It is shown that this class has very nice properties. For example, if MiAP(ni,0), i=1,2, then M1×M2AP(n1+n2,0). Moreover, MAP(n,0) if and only if each point of M has a local base of neighborhoods U with UAP(n,0). Using the properties of AP(n,0)-spaces, we generalize some results of Levin and Kato-Matsuhashi concerning the existence of residual sets of n-dimensional Lelek maps.
Keywords:Dimension  n-dimensional maps  n-dimensional Lelek maps  Dendrites  Cantor n-manifolds  General position properties
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