Glasnik Matematicki, Vol. 52, No. 1 (2017), 179-183.

GENERALIZED SUSPENSION THEOREM IN EXTENSION THEORY

Leonard R. Rubin

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.

2010 Mathematics Subject Classification.   54C55, 54C20.

Key words and phrases.   Absolute co-extensor, absolute extensor, absolute neighborhood extensor, CW-complex, extension theory, paracompact, shrinking a cover, stratifiable space, stratification, suspension.

DOI: 10.3336/gm.52.1.13

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