The hyperspace of finite subsets of a stratifiable space
Cauty, Robert ; Guo, Bao-Lin ; Sakai, Katsuro
Fundamenta Mathematicae, Tome 146 (1995), p. 1-9 / Harvested from The Polish Digital Mathematics Library
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It is shown that the hyperspace of non-empty finite subsets of a space X is an ANR (an AR) for stratifiable spaces if and only if X is a 2-hyper-locally-connected (and connected) stratifiable space.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:212071 
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Cauty, Robert; Guo, Bao-Lin; Sakai, Katsuro. The hyperspace of finite subsets of a stratifiable space. Fundamenta Mathematicae, Tome 146 (1995) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv147i1p1bwm/

[00000] [Bo1] C. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16. | Zbl 0175.19802

[00001] [Bo2] C. R. Borges, A study of absolute extensor spaces, ibid. 31 (1969), 609-617; corrigenda, ibid. 50 (1974), 29-30.

[00002] [Bo3] C. R. Borges, Connectivity of function spaces, Canad. J. Math. 23 (1971), 759-763. | Zbl 0207.43201

[00003] [Ca1] R. Cauty, Une généralisation du théorème de Borsuk-Whitehead-Hanner aux espaces stratifiables, C. R. Acad. Sci. Paris Sér. A 275 (1972), 271-275. | Zbl 0238.54016

[00004] [Ca2] R. Cauty, Produits symétriques de rétractes absolus de voisinage, ibid. 276 (1973), 359-361. | Zbl 0247.54012

[00005] [Ca3] R. Cauty, Rétractions dans les espaces stratifiables, Bull. Soc. Math. France 102 (1974), 129-149. | Zbl 0292.54015

[00006] [Ce] J. G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105-126. | Zbl 0103.39101

[00007] [CN] D. Curtis and Nguyen To Nhu, Hyperspaces of finite subsets which are homeomorphic to ℵ0-dimensional linear metric spaces, Topology Appl. 19 (1985), 251-260. | Zbl 0587.54015

[00008] [Du] J. Dugundji, Locally equiconnected spaces and absolute neighborhood retracts, Fund. Math. 57 (1965), 187-193. | Zbl 0151.30301

[00009] [GS] B.-L. Guo and K. Sakai, Hyperspaces of CW-complexes, Fund. Math. 143 (1993), 23-40. | Zbl 0845.54008

[00010] [Ja] J. W. Jaworowski, Symmetric products of ANR's, Math. Ann. 192 (1971), 173-176. | Zbl 0206.25002

[00011] [Ke] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36. | Zbl 0061.40107

[00012] [Mi] E. Michael, Topologies on spaces of subsets, ibid. 71 (1951), 152-182.

[00013] [MK] T. Mizokami and T. Koiwa, On hyperspaces of compact and finite subsets, Bull. Joetsu Univ. Educ. 6 (1987), 1-14.

[00014] [Ng] Nguyen To Nhu, Investigating the ANR-property of metric spaces, Fund. Math. 124 (1984), 244-254. | Zbl 0573.54009

[00015] [Sa] S. San-ou, A note on Ξ-product, J. Math. Soc. Japan 29 (1977), 281-285.