International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 493290, 11 pages
http://dx.doi.org/10.1155/2011/493290
Research Article

Homeomorphisms of Compact Sets in Certain Hausdorff Spaces

Arthur D. Grainger

Department of Mathematics, Carnegie Hall, Room CR-152, Morgan State University, Cold Spring Lane and Hillen Road, Baltimore, MD 21239, USA

Received 5 January 2011; Accepted 18 April 2011

Academic Editor: Vladimir Mityushev

Copyright © 2011 Arthur D. Grainger. 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 construct a class of Hausdorff spaces (compact and noncompact) with the property that nonempty compact subsets of these spaces that have the same cardinality are homeomorphic. Also, it is shown that these spaces contain compact subsets that are infinite.