International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 24370, 12 pages

The compactificability classes: The behavior at infinity

Martin Maria Kovár

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

Received 15 October 2004; Revised 18 November 2005; Accepted 28 November 2005

Copyright © 2006 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.


We study the behavior of certain spaces and their compactificability classes at infinity. Among other results we show that every noncompact, locally compact, second countable Hausdorff space X such that each neighborhood of infinity (in the Alexandroff compactification) is uncountable, has 𝒞(X)=𝒞(). We also prove some criteria for (non-) comparability of the studied classes of mutual compactificability.