Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A completely regular space which is the $T_1$-complement of itself
HTML articles powered by AMS MathViewer

by Stephen Watson PDF
Proc. Amer. Math. Soc. 124 (1996), 1281-1284 Request permission

Abstract:

Two topologies $\tau$ and $\sigma$ on a fixed set are $T_{1}$-complements if $\tau \cap \sigma$ is the cofinite topology and $\tau \cup \sigma$ is a sub-base for the discrete topology. In 1967, Steiner and Steiner showed that of any two $T_{1}$-complements on a countable set, at least one is not Hausdorff. In 1969, Anderson and Stewart asked whether a Hausdorff topology on an uncountable set can have a Hausdorff $T_{1}$-complement. We construct two homeomorphic completely regular $T_{1}$-complementary topologies.
References
Similar Articles
Additional Information
  • Stephen Watson
  • Affiliation: Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3
  • Email: stephen.watson@mathstat.yorku.ca
  • Received by editor(s): July 1, 1992
  • Received by editor(s) in revised form: October 4, 1994
  • Additional Notes: This work has been supported by the Natural Sciences and Engineering Research Council of Canada
  • Communicated by: Franklin D. Tall
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 1281-1284
  • MSC (1991): Primary 54A10, 05C20; Secondary 54B15, 54A25
  • DOI: https://doi.org/10.1090/S0002-9939-96-03524-1
  • MathSciNet review: 1343729