International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 24370, 12 pages
doi:10.1155/IJMMS/2006/24370
The compactificability classes: The
behavior at infinity
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.
Abstract
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(ℝ). We also prove some criteria for
(non-) comparability of the studied classes of mutual
compactificability.