Hyperspaces of CW-complexes

Bao-Lin Guo; Katsuro Sakai

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 1, page 23-40
  • ISSN: 0016-2736

Abstract

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It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.

How to cite

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Guo, Bao-Lin, and Sakai, Katsuro. "Hyperspaces of CW-complexes." Fundamenta Mathematicae 143.1 (1993): 23-40. <http://eudml.org/doc/211990>.

@article{Guo1993,
abstract = {It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.},
author = {Guo, Bao-Lin, Sakai, Katsuro},
journal = {Fundamenta Mathematicae},
keywords = {CW-complex; hyperspace; the Vietoris topology; stratifiable space; AR(S); ANR(S); ; ; Vietoris topology},
language = {eng},
number = {1},
pages = {23-40},
title = {Hyperspaces of CW-complexes},
url = {http://eudml.org/doc/211990},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Guo, Bao-Lin
AU - Sakai, Katsuro
TI - Hyperspaces of CW-complexes
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 1
SP - 23
EP - 40
AB - It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.
LA - eng
KW - CW-complex; hyperspace; the Vietoris topology; stratifiable space; AR(S); ANR(S); ; ; Vietoris topology
UR - http://eudml.org/doc/211990
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. 
  3. [Bo3] C. R. Borges, Absolute extensor spaces: A correction and an answer, ibid. 50 (1974), 29-30. Zbl0276.54025
  4. [Bo4] C. R. Borges, Connectivity of function spaces, Canad. J. Math. 5 (1971), 759-763. Zbl0207.43201
  5. [Ca1] R. Cauty, Sur les sous-espaces des complexes simpliciaux, Bull. Soc. Math. France 100 (1972), 129-155. Zbl0243.54027
  6. [Ca2] R. Cauty, Sur le prolongement des fonctions continues à valeurs dans CW-complexes, C. R. Acad. Sci. Paris Sér. A 274 (1972), 35-37. Zbl0226.54011
  7. [Ca3] R. Cauty, Convexité topologique et prolongement des fonctions continues, Compositio Math. 27 (1973), 133-271. Zbl0275.54015
  8. [Ca4] R. Cauty, Rétraction dans les espaces stratifiables, Bull. Soc. Math. France 102 (1974), 129-149. Zbl0292.54015
  9. [Ca5] R. Cauty, Sur les espaces d'applications dans les CW-complexes, Arch. Math. (Basel) 27 (1976), 306-311. Zbl0328.54009
  10. [Ce] J. G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105-126. Zbl0103.39101
  11. [CP] D. W. Curtis and D. S. Patching, Hyperspaces of direct limits of locally compact metric spaces, Topology Appl. 29 (1988), 55-60. Zbl0661.54015
  12. [CP] D. W. Curtis and R. M. Schori, Hyperspaces of polyhedra are Hilbert cubes, Fund. Math. 99 (1978), 189-197. Zbl0397.54036
  13. [CS1] D. W. Curtis and R. M. Schori, Hyperspaces of Peano continua are Hilbert cubes, ibid. 101 (1978), 19-38. Zbl0409.54044
  14. [Gr] G. Gruenhage, Stratifiable spaces are M 2 , Topology Proc. 1 (1976), 221-226. Zbl0389.54019
  15. [Ju] H. J. K. Junnila, Neighbornets, Pacific J. Math. 76 (1978), 83-108. Zbl0353.54016
  16. [Ke] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36. Zbl0061.40107
  17. [Mi] T. Mizokami, On CF families and hyperspaces of compact subsets, Topology Appl. 35 (1990), 75-92. Zbl0715.54018
  18. [MK] T. Mizokami and K. Koiwa, On hyperspaces of compact and finite subsets, Bull. Joetsu Univ. of Education 6 (1987), 1-14. 
  19. [Ta] U. Tašmetov, On the connectedness of hyperspaces, Dokl. Akad. Nauk SSSR 215 (1974), 286-288 (in Russian); English transl.: Soviet Math. Dokl. 15 (1974), 502-504. Zbl0297.54009
  20. [Wo] M. Wojdysławski, Rétractes absolus et hyperespaces des continus, Fund. Math. 32 (1939), 184-192. Zbl0021.36001

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