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R1-Topological Spaces1

Published online by Cambridge University Press:  20 November 2018

M.G. Murdeshwar  and
S.A. Naimpally
M.G. Murdeshwar
Affiliation:
University of Alberta, Edmonton
S.A. Naimpally
Affiliation:
University of Alberta, Edmonton
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In his paper ″Indexed systems of neighborhoods for general topological spaces″ (Amer. Math. Monthly 68, (1961), 886–893), A.S. Davis defined a hierarchy of what he called regularity axioms. The R1 -axiom is independent of both T0 and T1, but is strictly weaker than T2. In this note, we propose to study the properties of the spaces satisfying the R1 -axiom. In particular, we will show that in many well-known results, the hypothesis can be weakened from T2 to R1, which is part of our motivation in studying R1 -spaces.

Type
Notes and Problems
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 4 , October 1966 , pp. 521 - 523
Copyright
Copyright © Canadian Mathematical Society 1966

Footnotes

1

Research partially supported by the Summer Research Institute of the Canadian Mathematical Congress.

References

1 Research partially supported by the Summer Research Institute of the Canadian Mathematical Congress.