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International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 1, Pages 197-200
Research notes

A class of completely regular spaces

Department of Mathematics, Åbo Akademi, Åbo 50 20500, Finland

Received 30 August 1983

Copyright © 1984 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we investigate topologies with ultrafilters having bases of open sets. It is shown that these topologies are completely regular. All results are obtained by using Richardson's compactification of convergence spaces. We also prove a non-existance of a dense convergence space compactification with lifting property.