Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-25T16:55:38.600Z Has data issue: false hasContentIssue false
  • English
  • Français

Moore Spaces, Semi-Metric Spaces and Continuous Mappings Connected with Them

Published online by Cambridge University Press:  20 November 2018

C. M. Pareek
C. M. Pareek*
Affiliation:
University of Saskatchewan, Regina, Saskatchewan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [1] Arhangel'skiĭ announced that any σ-paracompact p-space could be mapped onto a Moore space by a perfect map. However Burke [3] recently showed that this is not true in general and he gave an example of a T2, locally compact, σ-paracompact space which cannot be mapped onto a Moore space by a perfect map.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1033 - 1042
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Arhangel'skii, A. V., Mappings and spaces, Russian Math. Surveys 21 (1966), 115–162.Google Scholar
2. Bing, R. H., Metrization of topological spaces, Can. J. Math. 3 (1951), 175–186.Google Scholar
3. Burke, D. K., Subparacompact spaces, Proc. of the Washington State University conference on general topology (March 1970), 39-49.Google Scholar
4. Ceder, J. G., Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105–125.Google Scholar
5. McAuley, L. F., A note on complete collectionwise normality and paracompactness, Proc. Amer. Math. Soc. 9 (1958), 796–799.Google Scholar
6. Pareek, C. M., Characterization of p-spaces, Can. Math. Bull. 14 (1971), 459–460.Google Scholar
7. Ponomarev, V. I., On paracompact and finally compact spaces, Soviet Math. Dokl. 2 (1961), 1510–1512.Google Scholar