Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Characterizations of paracompact-like properties by means of set-valued semi-continuous selections


Author: Kazumi Miyazaki
Journal: Proc. Amer. Math. Soc. 129 (2001), 2777-2782
MSC (2000): Primary 54B20, 54C65
DOI: https://doi.org/10.1090/S0002-9939-01-06204-9
Published electronically: April 24, 2001
MathSciNet review: 1838802
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

We give a characterization of countably paracompact and collectionwise normal spaces by means of set-valued semi-continuous selections. This provides a positive answer to a problem of V. Gutev.


References [Enhancements On Off] (What's this?)

  • 1. J. Chaber, M. M. Čoban, and K. Nagami, On monotonic generalizations of Moore spaces, Čech complete spaces and 𝑝-spaces, Fund. Math. 84 (1974), no. 2, 107–119. MR 0343244
  • 2. M. M. Čoban, Multi-valued mappings and Borel sets. I, II, Trudy Moskov. Mat. Obšč. 22 (1970), 229–250; ibid. 23 (1970), 277–301. MR 0372812
  • 3. S. Ĭ. Nedev and M. M. Čoban, Factorization theorems for multivalued mappings, multivalued cross sections and topological dimension, Math. Balkanica 4 (1974), 457–460 (Russian). Papers presented at the Fifth Balkan Mathematical Congress (Belgrade, 1974). MR 0388328
  • 4. C. H. Dowker, Homotopy extension theorems, Proc. London. Math. Soc. 6 (1956), 100-116. MR 17:518f
  • 5. Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
  • 6. M. K. Fort, Jr., A unified theory of semi-continuity, Duke Math. J. 16 (1949), 237-246. MR 10:716f
  • 7. V. Gutev, Generic extensions of finite-valued u.s.c. selections, Topology and Appl. 104 (2000), 101-118. CMP 2001:01
  • 8. Valentin G. Gutev, Weak factorizations of continuous set-valued mappings, Topology Appl. 102 (2000), no. 1, 33–51. MR 1739262, https://doi.org/10.1016/S0166-8641(98)00139-4
  • 9. -, Selections of set-valued mappings and hyperspace topologies, (unpublished).
  • 10. Valentin Gutev and Tsugunori Nogura, Selections for Vietoris-like hyperspace topologies, Proc. London Math. Soc. (3) 80 (2000), no. 1, 235–256. MR 1719152, https://doi.org/10.1112/S0024611500012107
  • 11. E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182. MR 13:54f
  • 12. E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J 26 (1959), 647–651. MR 0109343
  • 13. -, Continuous selection I, Ann. Math. 63 (1956), 361-382. MR 17:990e
  • 14. E. Michael, Complete spaces and tri-quotient maps, Illinois J. Math. 21 (1977), no. 3, 716–733. MR 0467688
  • 15. Stoyan Ĭ. Nedev, Selection and factorization theorems for set-valued mappings, Serdica 6 (1980), no. 4, 291–317 (1981). MR 644284

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54B20, 54C65

Retrieve articles in all journals with MSC (2000): 54B20, 54C65


Additional Information

Kazumi Miyazaki
Affiliation: Department of Mathematical Sciences, Faculty of Sciences, Ehime University, Matsuyama 790-8577, Japan
Email: BZQ22206@nifty.ne.jp

DOI: https://doi.org/10.1090/S0002-9939-01-06204-9
Keywords: Hyperspace, selection, semi-continuous
Received by editor(s): May 12, 1999
Received by editor(s) in revised form: December 12, 1999
Published electronically: April 24, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society