Operation on laklaklak-closed sets (original) (raw)

Operation on Ω̂-closed sets

2019

This work is based on operation in a topological space. An operation has been extended to the class of Ω̂-open sets. The new class of γΩ̂-open sets has been introduced and two kinds of closures such as, γΩ̂Cl and (Ω̂Cl)γ are studied. Necessary basic properties have been derived. Moreover, Ω̂-regular operation on Ω̂O(X ,τ) has been introduced in which intersection of any two γΩ̂-closed sets is γΩ̂-closed. Also three types of separation axioms are defined and few results on them have been derived.

Operation-Separation Axioms via Α-Open Sets

2016

The purpose of this paper is to investigate several types of separation axioms in topological spaces and study some of the essential properties of such spaces. Moreover, we investigate their relationship to some other known separation axioms and some counterexamples. 2010 Mathematics Subject Classification: 30C45.

A Class of Functions and Separation Axioms with Respect to an Operation

2009

In this paper, a new kind of set called a γ-β-open set is introduced and investigated using the γ-operator due to Ogata (H. Ogata, Operations on topological spaces and associated topology, Math. Japonica 36 (1), 175-184, 1991). Such sets are used for studying new types of mappings, viz. γ-continuous, γ-β-continuous, γ-β-open, γ-β-closed, γ-βgeneralized mappings, etc. A decomposition theorem for γ-continuous mappings, as well as a characterization of continuous mapping are obtained in terms of γ-β-continuous mappings. Finally, new separation axioms: γ-β-Ti (i = 0, 1 2 , 1, 2), γ-β-regularity and γ-β-normality are investigated along with the result that every topological space is γ-βT 1 2 .

Some types of separation axioms in topological spaces

In this paper, we introduce some types of separation axioms via ω-open sets, namely ω-regular, completely ω-regular and ω-normal space and investigate their fundamental properties, relationships and characterizations. The well-known Urysohn's Lemma and Tietze Extension Theorem are generalized to ω-normal spaces. We improve some known results. Also, some other concepts are generalized and studied via ω-open sets.

ON RGW⍺LC-SEPARATION AXIOMS IN TOPOLOGICAL SPACES.

The aim of this paper is to introduce and study two new classes of spaces, namely rgw⍺lc-𝜏0, rgw⍺lc-𝜏1, rgw⍺lc-𝜏2,rgw⍺lc-regular and rgw⍺lc-normal spaces and obtained their properties by utilizing rgw⍺lc-closed sets. Also we will present some characterizations of these spaces.

On New Separation Axioms Via γ-Open Sets

In this paper, we introduce two new classes of topological spaces called γ-R0 and γ-R1 spaces in terms of the concept of γ-open sets and investigate some of their fundamental properties.

Separation Axioms On Topological Spaces - A Unified Version

European Journal of Pure and Applied Mathematics, 2013

In this paper a new kind of sets called generalized closed sets are introduced and studied in a topological space by using the concept of operation in a topological space. Some of their properties are investigated. Finally, some characterizations of psig\psi_gpsig-regular, psig\psi_gpsig-normal spaces are given.

(Α,Β)-Semi Open Sets and Some New Generalized Separation Axioms

Let (X, τ) be a topological space and α, β : P (X) → P (X) be operators associated to τ , we introduce the concept of (α, β)-semi open sets and new generalized forms of separations by (α,β)-semi open sets. Also, we analyze the relations with some well known separation notions.

Operation-Separation Axioms via Γ-PS-Open Sets

2018

This paper defines some new γ-PSseparation axioms called γ-PS-Ti for i = 0, 1, 2 using γ-PS-open sets. Some theoretical results and properties for these γ-PSseparation axioms are obtained. Several examples are given to illustrate some of the results. AMS Subject Classification: 54A05, 54D10