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Semi-Hausdorff Spaces

Published online by Cambridge University Press:  20 November 2018

M.G. Murdeshwar  and
S.A. Naimpally
M.G. Murdeshwar
Affiliation:
University of Alberta, Edmonton and Iowa State University
S.A. Naimpally
Affiliation:
University of Alberta, Edmonton and Iowa State University
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It is well-known that in a Hausdorff space, a sequence has at most one limit, but that the converse is not true. The condition that every sequence have at most one limit will be called the semi-Hausdorff condition. We will prove that the semi-Hausdorff condition is strictly stronger than the T1 -axiom and is thus between the T1 and T2 axioms. In this note, we investigate into some properties of the spaces satisfying the semi-Hausdorff condition.

Type
Notes and Problems
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 3 , August 1966 , pp. 353 - 356
Copyright
Copyright © Canadian Mathematical Society 1966