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On finite-dimensional maps II

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
132
Issue
1
Identifiers
DOI: 10.1016/s0166-8641(02)00365-6
Keywords
  • Finite-Dimensional Maps
  • Set-Valued Maps
  • Selections
  • C-Space
Disciplines
  • Mathematics

Abstract

Abstract Let f :X→Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g :X→ I k=[0,1] k , where 1⩽ k⩽ ω: each g( f −1( y)), y∈ Y, is at most n-dimensional. It is shown that all maps g∈C(X, I n+1) with the above property form a dense G δ -set in the function space C(X, I n+1) equipped with the source limitation topology. Moreover, for every n+1⩽ m⩽ ω the space C(X, I m) contains a dense G δ -set of maps having this property.

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