H-closed Spaces and H-sets in the Convergence Setting

TL;DR

This paper explores H-closed spaces and H-sets within convergence theory, revealing their pretopological nature and extending the concept to pretopological spaces to analyze their properties.

Contribution

It introduces a convergence-theoretic framework for H-closed spaces and H-sets, and defines H-closedness for pretopological spaces, expanding the theoretical understanding.

Findings

H-closedness and H-sets are pretopological notions

Defined H-closedness for pretopological spaces

Analyzed properties of H-closed pretopological spaces

Abstract

We use convergence theory as the framework for studying H-closed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space are pretopological notions. Additionally, we define a version of H-closedness for pretopological spaces and investigate the properties of such a space.