# 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
- Disciplines

## 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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