Cauty, Robert; Guo, Bao-Lin; Sakai, Katsuro The hypersurface of finite subsets of a stratifiable space. (English) Zbl 0823.54014 Fundam. Math. 147, No. 1, 1-9 (1995). 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. Keywords:2-hyper-locally connected stratifiable space; \({\mathcal F} (X)\) of finite subsets of a stratifiable space \(X\) PDFBibTeX XMLCite \textit{R. Cauty} et al., Fundam. Math. 147, No. 1, 1--9 (1995; Zbl 0823.54014) Full Text: EuDML