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The hypersurface of finite subsets of a stratifiable space. (English) Zbl 0823.54014

The authors prove the following result: The space \({\mathcal F} (X)\) of finite subsets of a stratifiable space \(X\) with the Vietoris topology is an ANR (AR) for stratifiable spaces if and only if \(X\) is a 2-hyper- locally connected (and connected) stratifiable space.
Reviewer: C.R.Borges (Davis)

MSC:

54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
54B20 Hyperspaces in general topology
54E20 Stratifiable spaces, cosmic spaces, etc.
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