Semi Lamda*-Closed Sets and New Separation Axioms in Alexandroff Spaces

TL;DR

This paper explores semi Lamda*-closed sets and introduces new separation axioms in Alexandroff spaces, analyzing their properties and interrelations to deepen understanding of topological separation concepts.

Contribution

It introduces new separation axioms in Alexandroff spaces and investigates their properties and equivalences, expanding the theoretical framework of topology.

Findings

New separation axioms semi-Tw/4, semi-T3w/8, semi-T5w/8 introduced

Established relations and conditions for equivalence of these axioms

Enhanced understanding of semi Lamda*-closed sets in Alexandroff spaces

Abstract

Here we have studied the idea of semi Lamda*-closed sets and investigate some of their properties in spaces considered by A. D. Alexandroff [1]. We have introduced some new separation axioms namely semi-Tw/4, , semi-T3w/8, semi-T5w/8, and their inter-relation with semi-T0 and semi-T1. We have shown that under certain conditions these axioms are equivalent.