Some properties of I*-sequential topological space

TL;DR

This paper introduces and studies the properties of $\\mathcal{I}^{*}$-sequential topology on topological spaces, exploring its relation to other topologies and its implications for sequential continuity and compactness.

Contribution

It defines the $\mathcal{I}^{*}$-sequential topology, proves its relation to $\mathcal{I}$-sequential topology, and investigates key properties like continuity and compactness.

Findings

$\mathcal{I}^{*}$-sequential topology is finer than $\mathcal{I}$-sequential topology.

Established properties of $\mathcal{I}^{*}$-sequential continuity.

Analyzed $\mathcal{I}^{*}$-sequential compactness.

Abstract

In this paper, we will define $\mathcal{I}^{*}$-sequential topology on a topological space $(X,\tau)$ where $\mathcal{I}$ is an ideal of the subset of natural numbers $\mathbb{N}$. Besides the basic properties of the $\mathcal{I}^{*}$-sequential topology, we proved that $\mathcal{I}^{*}$-sequential topology is finer than $\mathcal{I}$-sequential topology. Further, we will discus main properties of $\mathcal{I}^{*}$ sequential continuity and $\mathcal{I}^{*}$ sequential compactness.