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

Semi-generalized Separation Axioms in topology

space, 2001

In this paper, we introduce and study a new class of separation axioms called semi-generalized separation axioms using semi-generalized open sets due to Bhattacharya and Lahari. The connections between these separation axioms and other existing well-known related semi separation axioms are also investigated.

Operation on semi generalized open sets with its separation axioms

The aim of this paper is to introduce the concept of an operation γ on the class of all semi-generalized open sets in topological spaces. Using this operation, we define a new concept called semi-generalized-γ-open (sg-γ-open) sets and study some of their related properties. We found that the relation between this new concept and sg-open set are independent. In addition, we study some separation axioms called sg-γ-Ti for i = 0, 1, 2. Some basic properties and relations of these separation axioms are obtained.

On Some New Types of Separation Axioms Via δ ∗-semiopen Sets

New trends in mathematical sciences, 2022

In this paper, we study different properties of δ *-semiopen set. We define the concept of δ *-semi generalized closed sets and present some characteristics. In addition, as applications to δ *-semi generalized closed set, we introduce δ *-semi T1 2 space and obtain some of their basic properties. Moreover, we defined the notions of δ *-semi symmetric space, δ *-semi difference sets and δ *-semi kernel of sets, and investigate some of their fundamental properties. At the latest, some new types of spaces are introduced and the relationships of these spaces are studied.

Some New Separation Axioms Via β-I-Open Sets

Annals of the Alexandru Ioan Cuza University - Mathematics, 2015

In this paper, β-I-open sets are used to define some weak separation axioms and to study some of their basic properties. The implications of these axioms among themselves and with the known axioms are investigated

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 Some Generalized Topologies Satisfying all Separation Axioms

Results in Mathematics, 2023

The properties of generalized topological spaces generated by some kind of density operators are presented. Moreover, the separation axioms of such generalized topological spaces are investigated. The examples of generalized topological spaces satisfing all separation axioms are included.

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.