Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T04:46:52.765Z Has data issue: false hasContentIssue false
  • English
  • Français

Quasicompactness and functionally Hausdorff spaces

Published online by Cambridge University Press:  09 April 2009

A. J. D'Aristotle
A. J. D'Aristotle
Affiliation:
Brooklyn College of the City University of New York State University College at Geneseo U.S.A.
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] Van Est and Freudenthal introduced and studied several new separation axioms for a topological space. One of these was the pτsq axiom: Given distinct points p and q of X, there exists a real continuous function f on X with f(p) ≠ f(q). They observed that the pτsq axiom lies strictly between the Hausdorff and completely regular axioms, and that it neither implies nor is implied by the T3 axiom.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 3 , May 1973 , pp. 319 - 324
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Van Est, W. T. and Freudenthal, H., ‘Trennung durch statige funktionen in topologischen räumen’, Indag. Math. 15 (1951), 359–368.Google Scholar
[2]Orrin, Frink, ‘Compactifications and semi-normal spaces,’ Amer. J. Math. 86 (1964), 602–607.Google Scholar
[3]Frolik, Z., ‘Generalizations of compact and Lindelöf spaces,’ Czech. Math. J. 9 (84), (1959), 172–217.CrossRefGoogle Scholar
[4]Gillman, L. and Jerison, M., Rings of continuous functions (Van Nostrand, New York, 1960).CrossRefGoogle Scholar
[5]Kelley, J. L., General topology (Van Nostrand, New York, 1955).Google Scholar
[6]Pervin, W. J., Foundations of general topology (Academic Press, New York, 1964).Google Scholar
[7]Proizvolov, V. V., ‘On one-to-one continuous mappings of topological spaces,’ Mat. Sb. (N. S.) 60 (110), (1965), 417–431.Google Scholar
[8]Rudin, W., Principles of mathematical analysis (McGraw-Hill, New York, 1964).Google Scholar
[9]Willard, S., General topology (Addison-Wesley, Reading, Massachusetts, 1970).Google Scholar