International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 3, Pages 24370, 12 p.
doi:10.1155/IJMMS/2006/24370
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
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.