Mutually Compactificable Topological Spaces

Kovár, Martin Maria

doi:https://doi.org/10.1155/2007/70671

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 070671 | https://doi.org/10.1155/2007/70671

Mutually Compactificable Topological Spaces

Martin Maria Kovár¹

Academic Editor: Lokenath Debnath

Received13 Jun 2006

Accepted12 Nov 2006

Published29 Mar 2007

Abstract

Two disjoint topological spaces X, Y are (T2-) mutually compactificable if there exists a compact (T2-) topology on K=X∪Y which coincides on X, Y with their original topologies such that the points x∈X, y∈Y 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.

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Copyright

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.

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