International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 22, Pages 3697-3701
Baire spaces, -spaces, and some properly hereditary properties
Department of Mathematics and Physics, Faculty of Arts and Science, Qatar University, P.O. Box 2713, Doha, Qatar
Received 11 October 2004; Revised 8 September 2005
Copyright © 2005 Adnan Al-Bsoul. 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.
A topological property is properly hereditary property if
whenever every proper subspace has the property, the whole space
has the property. In this note, we will study some topological
properties that are preserved by proper subspaces; in fact, we
will study the following topological properties: Baire spaces,
second category, sequentially compact, hemicompact, -normal, and spaces having dispersion points. Also, we
will solve some open problems raised by Al-Bsoul (2003) and Arenas
(1996) and conclude this note by some open problems.