Unification of generalized open sets on topological spaces

Authors: Noiri, T.1; Roy, B.2

Source: Acta Mathematica Hungarica, Volume 130, Number 4, March 2011 , pp. 349-357(9)

Publisher: Springer

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Abstract:

A new kind of sets called generalized -closed (briefly g -closed) sets are introduced and studied in a topological space by using the concept of generalized open sets introduced by Á. Császár. The class of all g -closed sets is strictly larger than the class of all -closed sets. Furthermore, g-closed sets (in the sense of N. Levine [17]) is a special type of g -closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of g -regular and g -normal spaces have been given.

Keywords: 54C08; 54C10; 54D10; 54D15; g -closed set;  g -normal space;  g -regular; -open set

Document Type: Research Article

DOI: http://dx.doi.org/10.1007/s10474-010-0010-1

Affiliations: 1: 2949-1 Shiokita-cho, Hinagu, Yatsushiro-shi, Kumamoto-ken, Japan, Email: t.noiri@nifty.com 2: Department of Mathematics, Women’s Christian College, 6, Greek Church Row, Kolkata-, 700 026, India, Email: bishwambhar_roy@yahoo.co.in

Publication date: March 1, 2011

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