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Coherent and strong expansions of spaces coincide

Sibe Mardešić — 1998

Fundamenta Mathematicae

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...

There Are No Essential Phantom Mappings from 1-dimensional CW-complexes

Sibe Mardešić — 2013

Bulletin of the Polish Academy of Sciences. Mathematics

A phantom mapping h from a space Z to a space Y is a mapping whose restrictions to compact subsets are homotopic to constant mappings. If the mapping h is not homotopic to a constant mapping, one speaks of an essential phantom mapping. The definition of (essential) phantom pairs of mappings is analogous. In the study of phantom mappings (phantom pairs of mappings), of primary interest is the case when Z and Y are CW-complexes. In a previous paper it was shown that there are no essential phantom...

Strong shape of the Stone-Čech compactification

Sibe Mardešić — 1992

Commentationes Mathematicae Universitatis Carolinae

J. Keesling has shown that for connected spaces X the natural inclusion e : X β X of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.

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