Compact-covering-properties of finite-to-one mappings
type: Item
instance of: scholarly article
title: Compact-covering-properties of finite-to-one mappings
zbMATH Open document ID: 0883.54017
DOI: 10.1016/S0166-8641(97)00021-7
author: Gabriel Debs
author: Jean Saint Raymond
published in: Topology and its Applications
publication date: 1998-03-05T00:00:00Z
review text: An inductively perfect map is one that is perfect when restricted to a suitable closed subset of its domain (it should remain surjective). Such maps are compact-covering (because preimages of compact sets are compact under perfect maps). In [Compact covering and game determinacy, Topology Appl. 68, 153-185 (1996; Zbl 0848.54024)] the authors showed that, given enough determinacy, this implication may be reversed in the class of separable metric spaces. In the present paper the authors investigate under what conditions countable-compact-covering maps are inductively perfect. The main results are: a negative answer for finite-to-one maps and a positive answer for at-most-\(n\)-to-one maps. The proof of the positive result involves a detailed study of certain kinds of multi-valued maps into the hyperspace of compact sets.
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 1088821
zbMATH Keywords: perfect mapping
zbMATH Keywords: inductively perfect mapping
zbMATH Keywords: countable-compact-covering mapping
reviewed by: K. P. Hart
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1088821