Lamda*-Closed sets and new separation axioms in Alexandroff spaces

TL;DR

This paper explores various generalized closed sets and introduces new separation axioms in Alexandroff spaces, expanding the understanding of their topological properties and classifications.

Contribution

It introduces a new separation axiom T-5omega/8 and investigates properties of g*-closed, g^tou-sets, and Lamda*-closed sets in Alexandroff spaces.

Findings

Defined and analyzed properties of g*-closed, g^tou-sets, Lamda*-closed sets

Studied existing separation axioms T-omega/4, T-3omega/8, T-omega

Proposed and characterized a new separation axiom T-5omega/8

Abstract

Here we have studied the ideas of g*-closed sets, g^tou -sets and Lamda*-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied few separation axioms like T-omega/4,T-3omega/8, T-omega in Alexandroff spaces and have introduced a new separation axiom namely T-5omega/8 axiom in this space.