Sp-Separation Axioms

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.

Journal of emerging technologies and innovative research, 2021

The aim of this paper is to introduce and study some new types of separation axioms such as -T0, -T1, -T2, -R0 and -R1 axioms in topological spaces by using -open set. The relationships among -T0, -T1, -T2 and some other separation axioms are investigated.

European Journal of Pure and Applied Mathematics, 2012

In this paper, we introduce new separations axioms $\Lambda_{r}$-$R_{0}$, $\Lambda_{r}$-$R_{1}$ and $\Lambda_{r}$-$D_{k}$, and study their properties.

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.

2013

In this paper, we define some new types of separation axioms in topological spaces by using g b-open set also the concept of g b-R 0 and g b-R 1 are introduced. Several properties of these spaces are investigated.

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 $\psi_g$-regular, $\psi_g$-normal spaces are given.

JOURNAL OF EDUCATION AND SCIENCE

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.

Communications in Mathematics and Applications, 2021

This paper introduces separation axioms using \\(\\theta\\)-sgp-open sets in topological spaces. We also focus on some of their basic properties and also made the implication of these axioms among themselves and with other known axioms. Also we investigated characterizations of these axioms. It also introduces the concept of sober \\(\\theta\\)-sgp-\\(R_0\\) spaces.

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.