Open AccessApplications of operations on generalized topological spaces
Author(s) -
Bishwambhar Roy,
Takashi Noiri
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m3/96-104
Subject(s) - closure operator , closure (psychology) , closed set , mathematics , operator (biology) , axiom , open set , topological space , relation (database) , pure mathematics , set (abstract data type) , separation axiom , discrete mathematics , topology (electrical circuits) , computer science , combinatorics , data mining , geometry , market economy , biochemistry , chemistry , repressor , transcription factor , programming language , economics , gene
In this paper γµ -open sets and γµ -closed sets in a GTS (X, µ) have been studied, where γµ is an operation from µ to P(X). In general, collection of γµ -open sets is smaller than the collection of µ-open sets. The condition under which both are same are also established here. Some properties of such sets have been discussed. Some closure like operators are also defined and their properties are discussed. The relation between similar types of closure operators on the GTS (X, µ) has been established. The condition under which the newly defined closure like operator is a Kuratowski closure operator is given. We have also defined a generalized type of closed sets termed as γµ -generalized closed set with the help of this newly defined closure operator and discussed some basic properties of such sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have shown some preservation theorems of such generalized concepts.