The hyperspace of finite subsets of a stratifiable space

Robert Cauty; Bao-Lin Guo; Katsuro Sakai

Fundamenta Mathematicae (1995)

  • Volume: 147, Issue: 1, page 1-9
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Cauty, Robert, Guo, Bao-Lin, and Sakai, Katsuro. "The hyperspace of finite subsets of a stratifiable space." Fundamenta Mathematicae 147.1 (1995): 1-9. <http://eudml.org/doc/212071>.

@article{Cauty1995,
abstract = {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.},
author = {Cauty, Robert, Guo, Bao-Lin, Sakai, Katsuro},
journal = {Fundamenta Mathematicae},
keywords = {hyperspace; the Vietoris topology; stratifiable space; AR(S), ANR(S); 2-hyper-locally-connected; 2-hyper-locally connected stratifiable space; of finite subsets of a stratifiable space },
language = {eng},
number = {1},
pages = {1-9},
title = {The hyperspace of finite subsets of a stratifiable space},
url = {http://eudml.org/doc/212071},
volume = {147},
year = {1995},
}

TY - JOUR
AU - Cauty, Robert
AU - Guo, Bao-Lin
AU - Sakai, Katsuro
TI - The hyperspace of finite subsets of a stratifiable space
JO - Fundamenta Mathematicae
PY - 1995
VL - 147
IS - 1
SP - 1
EP - 9
AB - 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.
LA - eng
KW - hyperspace; the Vietoris topology; stratifiable space; AR(S), ANR(S); 2-hyper-locally-connected; 2-hyper-locally connected stratifiable space; of finite subsets of a stratifiable space
UR - http://eudml.org/doc/212071
ER -

References

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  1. [Bo1] C. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16. Zbl0175.19802
  2. [Bo2] C. R. Borges, A study of absolute extensor spaces, ibid. 31 (1969), 609-617; corrigenda, ibid. 50 (1974), 29-30. 
  3. [Bo3] C. R. Borges, Connectivity of function spaces, Canad. J. Math. 23 (1971), 759-763. Zbl0207.43201
  4. [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. Zbl0238.54016
  5. [Ca2] R. Cauty, Produits symétriques de rétractes absolus de voisinage, ibid. 276 (1973), 359-361. Zbl0247.54012
  6. [Ca3] R. Cauty, Rétractions dans les espaces stratifiables, Bull. Soc. Math. France 102 (1974), 129-149. Zbl0292.54015
  7. [Ce] J. G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105-126. Zbl0103.39101
  8. [CN] D. Curtis and Nguyen To Nhu, Hyperspaces of finite subsets which are homeomorphic to ℵ 0 -dimensional linear metric spaces, Topology Appl. 19 (1985), 251-260. Zbl0587.54015
  9. [Du] J. Dugundji, Locally equiconnected spaces and absolute neighborhood retracts, Fund. Math. 57 (1965), 187-193. Zbl0151.30301
  10. [GS] B.-L. Guo and K. Sakai, Hyperspaces of CW-complexes, Fund. Math. 143 (1993), 23-40. Zbl0845.54008
  11. [Ja] J. W. Jaworowski, Symmetric products of ANR's, Math. Ann. 192 (1971), 173-176. Zbl0206.25002
  12. [Ke] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36. Zbl0061.40107
  13. [Mi] E. Michael, Topologies on spaces of subsets, ibid. 71 (1951), 152-182. 
  14. [MK] T. Mizokami and T. Koiwa, On hyperspaces of compact and finite subsets, Bull. Joetsu Univ. Educ. 6 (1987), 1-14. 
  15. [Ng] Nguyen To Nhu, Investigating the ANR-property of metric spaces, Fund. Math. 124 (1984), 244-254. Zbl0573.54009
  16. [Sa] S. San-ou, A note on Ξ-product, J. Math. Soc. Japan 29 (1977), 281-285. 

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