International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 70671, 10 pages
Research Article

Mutually Compactificable Topological Spaces

Martin Maria Kovár

Department of Mathematics, Faculty of Electrical Engineering and Communication, University of Technology, Technická 8, Brno 616 69, Czech Republic

Received 13 June 2006; Accepted 12 November 2006

Academic Editor: Lokenath Debnath

Copyright © 2007 Martin Maria Kovár. 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.


Two disjoint topological spaces X, Y are (T2-) mutually compactificable if there exists a compact (T2-) topology on K=XY which coincides on X, Y with their original topologies such that the points xX, yY have open disjoint neighborhoods in K. This paper, the first one from a series, contains some initial investigations of the notion. Some key properties are the following: a topological space is mutually compactificable with some space if and only if it is θ-regular. A regular space on which every real-valued continuous function is constant is mutually compactificable with no S2-space. On the other hand, there exists a regular non-T3.5 space which is mutually compactificable with the infinite countable discrete space.