Accomplishments

Lightly Pre Normal Spaces


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Category
Articles
Authors
Publisher
Society For The Progress Of Science
Publishing Date
01-Oct-2007
volume
XXXIII M
Issue
4
Pages
1359-1364
  • Abstract

The concepts of lightly normal spaces and p-normal spaces are weaker form of normality . A topological space is called lightly normal[13] if for each pair of disjoint a closed set A and a zero set B, there exists disjoint open sets U and V such that A is a subset of U and B is a subset of V. A topological space is called p-normal space[10,11] if for each pair of disjoint closed sets A and B, there exists disjoint preopen sets U and V such that A is a subset of U and B is a subset of V. In this paper we have introduced a new concept , called lightly pre-normal space which is a generalization of both the above concepts . A topological space is called lightly pre normal if for each pair of disjoint a closed set A and a zero set B, there exists disjoint preopen sets U and V such that Ais a subset of U and B is a subset of V. Clearly every p-normal and lightly normal spaces are lightly pre normal. These spaces are characterized with the help of preclosure and gp-open sets and are preserved under continuous, preopen, pre gp-closed surjections and M-preclosed continuous surjections. Some other properties of these and their relation to other concepts of normality are also studied.