engleski

Coherent and strong expansions of spaces coincide

In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. Lisica and S.Mardešić an essential role is played by coherent polyhedral (ANR) expansion 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.

coherent expansion ; coherent homotopy ; inverse system ; strong expansion ; strong shape

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