A Note on Some Generalized Closed Sets in Bitopological Spaces Associated to Digraphs

K Kannan

doi:10.1155/2012/508580

Abstract

Many investigations are undergoing of the relationship between topological spaces and graph theory. The aim of this short communication is to study the nature and properties of some generalized closed sets in the bitopological spaces associated to the digraph. In particular, some relations between generalized closed sets in the bitopological spaces associated to the digraph are characterized.

Highlights

Concerning the applications of bitopological spaces, there are many approaches to the sets equipped with two topologies of which one may occasionally be finer than the other in analysis, potential theory, directed graphs, and general topology
Lukes 1 formulated certain new methods to be used in discussing fine topologies, especially in analysis and potential theory in 1977 and one of the properties introduced by him is Lusin-Menchoff property of the fine topologies
We have discussed the nature and properties of some generalized closed sets in the bitopological spaces associated to the digraphs in this short communication

Summary

Introduction

Concerning the applications of bitopological spaces, there are many approaches to the sets equipped with two topologies of which one may occasionally be finer than the other in analysis, potential theory, directed graphs, and general topology. Bhargava and Ahlborn 3 investigated certain tieups between the theory of directed graphs and point set topology They obtained several theorems relating connectedness and accessibility properties of a directed graph to the properties of the topology associated to that digraph. They investigated these topologies in terms of closure, kernal, and core operators. Fukutake 8 defined one kind of semiopen sets in bitopological spaces and studied their properties in 1989 He introduced generalized closed sets and pairwise generalized closure operator 9 in bitopological spaces in 1986. Some relations between generalized closed sets in the bitopological spaces associated to the digraph are characterized

Preliminaries

Relations between Some Generalized Closed Sets

Conclusion