Acta Mathematica Hungarica

, Volume 130, Issue 4, pp 349–357

Unification of generalized open sets on topological spaces


DOI: 10.1007/s10474-010-0010-1

Cite this article as:
Noiri, T. & Roy, B. Acta Math Hung (2011) 130: 349. doi:10.1007/s10474-010-0010-1


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

Key words and phrases

μ-open set gμ-closed set μg-regular μg-normal space 

2000 Mathematics Subject Classification

54D10 54D15 54C08 54C10 

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2010

Authors and Affiliations

  1. 1.Yatsushiro-shiJapan
  2. 2.Department of MathematicsWomen’s Christian CollegeKolkata-India