Coherent and strong expansions of spaces coincide
Tom 158 / 1998
Fundamenta Mathematicae 158 (1998), 69-80
DOI: 10.4064/fm-158-1-69-80
Streszczenie
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.
