Separation Axioms Weaker Than T1

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.

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.

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.

Journal of Computer Science & Computational Mathematics

In this paper we shall improve the definition of "properly hereditary property" which raised previously [1] and we shall prove that the topological properties: Functionally Hausdorff, , completely regular, normal, perfectly normal, S2, ∞ , locally connected, locally strongly connected, totally disconnected and Riesz separation axiom: TR are properly hereditary properties.

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.

2012

In this paper Sp-open sets are used to define some new types of separation axioms in topological spaces. The implications of these separation axioms among themselves with some other separation axioms are obtained. Also their basic properties and characterizations are investigated.

International Journal of Research -GRANTHAALAYAH

The purpose of this paper is to introduce weak separation axioms via sgp-closed sets in topological spaces and study some of their properties.

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, 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.