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A Definition of Separation Axiom

Published online by Cambridge University Press:  20 November 2018

T. Cramer
T. Cramer*
Affiliation:
University of British Columbia
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Extract

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Several separation axioms, defined in terms of continuous functions, were examined by van Est and Freudenthal [3], in 1951. Since that time, a number of new topological properties which were called separation axioms were defined by Aull and Thron [1], and later by Robinson and Wu [2], This paper gives a general definition of separation axiom, defined in terms of continuous functions, and shows that the standard separation axioms, and all but one of these new topological properties, fit this definition.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 485 - 491
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Aull, C. E. and Thron, W. J., Separation axioms between T0 and T1, Indagationes Math. 24 (1962), 26-37.Google Scholar
2. Robinson, S. M. and Wu, Y. C., A note on separation axioms weaker than T1, J. Australian Math. Soc. 9 (1969), 233-236.Google Scholar
3. van, W. T. Est and Freudenthal, H., Trennung durch stetige Funktionen in topologischen Raumen, Indagationes Math. 15, 359-368 (1951).Google Scholar