IJPAM: Volume 41, No. 5 (2007)

APPLICATIONS ON SIMPLE EXPANSIONS OF TOPOLOGY

A.M. Kozae
Department of Mathematics
Faculty of Science
Tanta University
Tanta, 31527, EGYPT
e-mail: akozae55@yahoo.com


Abstract.For a topological space $(X,\tau )$ and non open set $B$, the topology $\tau (B)$ generated by the class $\tau \cup \{B\}$ is finer than $\tau $. This finer topology together with an operation $\gamma :\tau \buildrel \over \longrightarrow P(X)$ are applied to introduce the concept of $(B,\gamma )$-generalized closed sets. Five well known types of generalized closed sets are special cases of the suggested concept. Also, new forms can arise by suitable choice of $B$ and $\gamma $. The closure operator with respect to $\tau (B)$ is used to initiate a new type of near open sets called $B$-preopen sets, some properties and characterizations for this class of near open sets are obtained.

Received: July 26, 2007

AMS Subject Classification: 46A03

Key Words and Phrases: topological space, generalized closed sets, preopen sets

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 5