Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T18:36:52.375Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on boundedly countably paracompact spaces

Part of: Fairly general properties

Published online by Cambridge University Press:  26 February 2010

P. Fletcher ,
R. A. McCoy  and
R. Slover
P. Fletcher
Affiliation:
Department of Mathematics, College of Arts and Science, Virginia Polytechnic Institute, Blacksburg, Virginia, 24061, U.S.A.
R. A. McCoy
Affiliation:
Department of Mathematics, College of Arts and Science, Virginia Polytechnic Institute, Blacksburg, Virginia, 24061, U.S.A.
R. Slover
Affiliation:
Department of Mathematics, College of Arts and Science, Virginia Polytechnic Institute, Blacksburg, Virginia, 24061, U.S.A.
Get access

Extract

The concepts of bounded paracompactness and bounded metacompactness were introduced and studied in [3]. In this paper we define bounded full normality and show that this concept is equivalent to bounded paracompactness.

It is known that countable paracompactness and countable metacompactness are equivalent properties in a normal space. We show that bounded countable metacompactness is equivalent to bounded countable paracompactness in a normal space and that bounded countable paracompactness is equivalent to bounded paracompactness in a hereditarily paracompact space.

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.)
Type
Research Article
Information
Mathematika , Volume 18 , Issue 2 , December 1971 , pp. 168 - 171
Copyright
Copyright © University College London 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Dowker, C. H., “Mapping theorems for non-compact spaces ”, Amer. J. Math., 69 (1947), 200–242.CrossRefGoogle Scholar
2.Dowker, C. H., “On countably paracompact spaces ”, Canadian J. Math., 3 (1951), 219–224.CrossRefGoogle Scholar
3.Fletcher, P., McCoy, R. A. and Slover, R., “On boundedly metacompact and boundedly paracompact spaces ”, Proc. Amer. Math. Soc., 25 (1970), 335–342.CrossRefGoogle Scholar
4.Morita, K., “On the dimension of normal spaces, I ”, Japan. J. Math., 20 (1950), 5–36.CrossRefGoogle Scholar
5.Stone, A. H., “Paracompactness and product spaces ”, Bull. Amer. Math. Soc., 54 (1948), 977–982.CrossRefGoogle Scholar
6.Rudin, M. E., “A normal space X for which X x I is not normal ”, Bull. Amer. Math. Soc., 77 (1971), 246.CrossRefGoogle Scholar