On GSI2-convergence in T0-spaces

TL;DR

This paper introduces GSI2-convergence and strongly QI2-continuity in T0-spaces, establishing conditions under which GSI2-convergence is topological in irreducible complete T0-spaces.

Contribution

It defines GSI2-convergence and strongly QI2-continuity, and proves their equivalence in certain classes of T0-spaces.

Findings

GSI2-convergence in T0-spaces is topological iff the space is strongly QI2-continuous.

Established the relationship between GSI2-convergence and QI2-continuity.

Characterized irreducible complete T0-spaces in terms of these concepts.

Abstract

In this paper,we introduce the concept of GSI$_2$-convergence in $T_0$ spaces and the related concept of (strongly) QI$_2$-continuous spaces. It is proved that if GSI$_2$-convergence in $X$ is topological iff $X$ is strongly QI$_2$-continuous for any irreducible complete $T_0$ space $X$.