Approximation by light maps and parametric Lelek maps |
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Authors: | Taras Banakh Vesko Valov |
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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 |
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Abstract: | The class of metrizable spaces M with the following approximation property is introduced and investigated: M∈AP(n,0) if for every ε>0 and a map g:In→M there exists a 0-dimensional map g′:In→M which is ε-homotopic to g. It is shown that this class has very nice properties. For example, if Mi∈AP(ni,0), i=1,2, then M1×M2∈AP(n1+n2,0). Moreover, M∈AP(n,0) if and only if each point of M has a local base of neighborhoods U with U∈AP(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. |
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Keywords: | Dimension n-dimensional maps n-dimensional Lelek maps Dendrites Cantor n-manifolds General position properties |
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