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ArticleOriginal scientific text

Title

Coherent and strong expansions of spaces coincide

Authors 1

Affiliations

  1. Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10.000 Zagreb, Croatia

Abstract

In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. T. Lisitsa and S. Mardešić [LM1-3] an essential role is played by coherent polyhedral (ANR) expansions of spaces. Such expansions always exist, because every space admits a polyhedral resolution, resolutions are strong expansions and strong expansions are always coherent. The purpose of this paper is to prove that conversely, every coherent polyhedral (ANR) expansion is a strong expansion. This result is obtained by showing that a mapping of a space into a system, which is coherently dominated by a strong expansion, is itself a strong expansion.

Keywords

ENG
coherent expansion, coherent homotopy, inverse system, strong expansion, strong shape

Bibliography

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Fundamenta Mathematicae
1998/158/1
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Pages:
69-80
Main language of publication
English
Received
1997-10-01
Published
1998
Exact and natural sciences