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Characterizations of p-Spaces

Published online by Cambridge University Press:  20 November 2018

C. M. Pareek
C. M. Pareek*
Affiliation:
University of Saskatchewan, Regina, Saskatchewan
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The concept of p-space is quite recent. It was introduced by Arhangel'skii [2]. The definition of p-space given in [2] involves compactification of the space. In view of the interesting properties of p-spaces obtained in [2], Alexadroff [1] suggested a problem of finding a direct intrinsic definition (without appeal to compactification). The main aim of this note is to answer the above problem.

I am grateful to Dr. S. K. Kaul for his comments.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 459 - 460
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Alexandroff, P. S., On some basic directions in general topology, Russian Math. Surveys 19 (1964), 1-39.Google Scholar
2. Arhangel'skii, A. V., A class of spaces containing all metric and locally compact spaces, Mat. Sb. 67 (1965), 55-85.Google Scholar
3. Engelking, E., Outline of general topology, North-Holland, Amsterdam, 1968.Google Scholar
4. Tamano, H., On compactifications, J. Math. Kyoto Univ. 1–2 (1962), 162-193.Google Scholar