International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 527106, 5 pages
doi:10.1155/2008/527106
Research Article
Some Characterizations of Open, Closed, and Continuous Mappings
Department of Mathematics, Faculty of Physical Sciences, Punjabi University, Patiala 147002, India
Received 9 October 2007; Accepted 19 January 2008
Academic Editor: Sehie Park
Copyright © 2008 Navpreet Singh Noorie and Rajni Bala. 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 obtain new characterizations of open maps in terms of closures, of closed maps in terms of interiors, and of continuous maps in terms of interiors. Further open (closed) onto maps
f:X→Y are described in terms of images under f of certain closed (open) sets in X. Continuity of (onto) maps is also characterized in terms of saturated sets.