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)

 
 

 

A note on subparacompact spaces


Author: R. E. Hodel
Journal: Proc. Amer. Math. Soc. 25 (1970), 842-845
MSC: Primary 54.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0263024-4
MathSciNet review: 0263024
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main result in this paper states that every metacompact space in which every closed set is a $ {G_\delta }$ is subparacompact. The class of countably subparacompact spaces is introduced and several results about such spaces are proved.


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

  • [1] R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175-186. MR 13, 264. MR 0043449 (13:264f)
  • [2] D. K. Burke, On subparacompact spaces, Proc. Amer. Math. Soc. 23 (1969), 655-663. MR 0250269 (40:3508)
  • [3] G. Creede, Semi-stratifiable spaces, Topology Conference Arizona State University, Tempe, Ariz., 1967, pp. 318-323.
  • [4] J. Greever, On spaces in which every closed set is a $ {G_\delta }$, Proc. Japan Acad. 43 (1967), 445-447. MR 37 #2183. MR 0226594 (37:2183)
  • [5] -, On screenable topological spaces, Proc. Japan Acad. 44 (1968), 434-438. MR 37 #3520. MR 0227936 (37:3520)
  • [6] R. W. Heath, Screenability, pointwise paracompactness, and metrization of Moore spaces, Canad. J. Math. 16 (1964), 763-770. MR 29 #4033. MR 0166760 (29:4033)
  • [7] M. J. Mansfield, On countably paracompact normal spaces, Canad. J. Math. 9 (1957), 443-449. MR 19, 436. MR 0087921 (19:436e)
  • [8] L. F. McAuley, A note on complete collectionwise normality and paracompactness, Proc. Amer. Math. Soc. 9 (1958), 796-799. MR 20 #6086. MR 0099647 (20:6086)
  • [9] J. M. Worrell, Jr., The closed continuous images of metacompact topological spaces, Portugal. Math. 25 (1966), 175-179. MR 38 #676. MR 0232351 (38:676)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.50

Retrieve articles in all journals with MSC: 54.50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0263024-4
Keywords: Metacompact, $ {G_\delta }$-set, subparacompact, screenable, countably subparacompact, countably metacompact
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society