Abstract
AbstractThis paper deals with the concepts of ζδ(μ)-sets and (ζ,δ(μ))-closed sets in a strong generalized topological space and investigate properties of several low separation axioms of strong generalized topologies constructed by the families of these sets. Some properties of (ζ,δ(μ))-R0 and (ζ,δ(μ))-R1 strong generalized topological spaces will be given. Finally, several characterizations of weakly (ζ,δ(μ))-continuous functions are discussed.
Highlights
General topology is important in many fields of applied sciences as well as branches of mathematics
The theory of generalized topology, which was founded by Császár (Császár, 1997), is one of the most important development of general topology in recent years
Noiri and Roy (Noiri & Roy, 2011) introduced a new kind of sets called generalized μ-closed sets in a topological space by using the concept of generalized open sets introduced by Császár
Summary
General topology is important in many fields of applied sciences as well as branches of mathematics. A subset A of a strong generalized topological space ðX; μÞ is said to be generalized ðζ; δðμÞÞ-closed (briefly g-ðζ; δðμÞÞ-closed) set if cðζ;δðμÞÞðAÞ U whenever A U and U 2 ðζ; δðμÞÞO. A subset A of a strong generalized topological space ðX; μÞ is g-ðζ; δðμÞÞ-closed if and only if cðζ;δðμÞÞðAÞ À A contains no non-empty ðζ; δðμÞÞ-closed set.
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