International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 853870, 10 pages
http://dx.doi.org/10.1155/2011/853870
Research Article

𝑊 𝜃 𝑔 -Closed and 𝑊 𝛿 𝑔 -Closed in [ 𝟎 , 𝟏 ] -Topological Spaces

M. E. El-Shafei1 and A. H. Zakari2

1Department of Mathematics, Mansoura University, P.O. Box 35516, Mansoura 35516, Egypt
2Department of Mathematics, Jazan University, P.O. Box 100, Jaza, Damad, Saudi Arabia

Received 8 June 2010; Accepted 14 September 2010

Academic Editor: Ayman Badawi

Copyright © 2011 M. E. El-Shafei and A. H. Zakari. 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 investigate various classes of generalized closed fuzzy sets in [ 0 , 1 ] -topological spaces, namely, 𝑊 𝜃 𝑔 -closed fuzzy sets and 𝑊 𝛿 𝑔 -closed fuzzy sets. Also, we introduce a new separation axiom 𝐹 𝑇 ∗ 3 / 4 of the [ 0 , 1 ] -topological spaces, and we prove that every 𝐹 𝑇 ∗ 3 / 4 -space is a 𝐹 𝑇 3 / 4 -space. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy mappings.