Geodesic
Coherent and strong expansions of spaces coincide
Fundamenta Mathematicae, Tome 158 (1998) no. 1, pp. 69-80

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI

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.
DOI : 10.4064/fm-158-1-69-80
Keywords: coherent expansion, coherent homotopy, inverse system, strong expansion, strong shape 
Sibe Mardešić. Coherent and strong expansions of spaces coincide. Fundamenta Mathematicae, Tome 158 (1998) no. 1, pp. 69-80. doi: 10.4064/fm-158-1-69-80
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