Operation approaches on \alpha-\gamma-open sets in topological spaces

Kalaivani, N.; SaiSundaraKrishnan, G.

doi:10.12988/ijma.2013.13045

Cited by 13 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Just as the concepts of T, g-T-interior 1 operators in T -spaces (ordinary and generalized interior operators in ordinary topological spaces) and T, g-T-closure operators in T -spaces (ordinary and generalized closure operators in ordinary topological spaces) are essential operators in the study of T-sets in T -spaces (arbitrary sets in ordinary topological spaces) [CJK04,Cs6,Cs5,Cs8,Cs7,GS17,JN19,Kal13,Lev70,Lev63,Lev61,MG16], so are the concepts of T g , g-T g -interior operators in T g -spaces (ordinary and generalized interior operators in generalized topological spaces) and T g , g-T g -closure operators in T g -spaces (ordinary and generalized closure operators in generalized topological spaces) essential operators in the study of T g -sets in T g -spaces (arbitrary sets in generalized topological spaces) [DB11,GS14,Min10,Min05,Mus17].…”

Section: Introductionmentioning

confidence: 99%

Theory of g-Tg-Interior and g-Tg-Closure Operators: Definitions, Essential Properties, and Commutativity

Khodabocus¹,

Sookia²

2019

Preprint

View full text Add to dashboard Cite

In a generalized topological space Tg = (Ω, Tg), ordinary interior and ordinary closure operators intg, clg : P (Ω) −→ P (Ω), respectively, are defined in terms of ordinary sets. In order to let these operators be as general and unified a manner as possible, and so to prove as many generalized forms of some of the most important theorems in generalized topological spaces as possible, thereby attaining desirable and interesting results, the present au- thors have defined the notions of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in terms of a new class of generalized sets which they studied earlier and studied their essen- tial properties and commutativity. The outstanding result to which the study has led to is: g-Intg : P (Ω) −→ P (Ω) is finer (or, larger, stronger) than intg : P (Ω) −→ P (Ω) and g-Clg : P (Ω) −→ P (Ω) is coarser (or, smal ler, weaker) than clg : P (Ω) −→ P (Ω). The elements supporting this fact are reported therein as a source of inspiration for more generalized operations.

show abstract