Original scientific paper

https://doi.org/10.3336/gm.52.1.13

Generalized suspension theorem in extension theory

Leonard R. Rubin orcid.org/0000-0002-1108-0267 ; Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA

Abstract

A. Dranishnikov proved that for each CW-complex K and metrizable compactum X with Xτ K, it is true that (X × I)τ(Σ K). Here, Σ K means the suspension of K in the CW-category, and by X τ K we mean that K is an absolute extensor for X. We are going to generalize this result so that X could be either a stratifiable space or a compact Hausdorff space. Since all metrizable spaces are stratifiable, then our result generalizes Dranishnikov's.

Keywords

Absolute co-extensor; absolute extensor; absolute neighborhood extensor; CW-complex; extension theory; paracompact, shrinking a cover; stratifiable space; stratification; suspension

Hrčak ID:

183131

URI

https://hrcak.srce.hr/183131

Publication date:

21.6.2017.

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