Compact-bounded topological groups

TL;DR

This paper investigates two specific subclasses of feebly compact spaces within (para)topological groups, namely compact-bounded and weakly compact-bounded spaces, and explores their properties and related subsets.

Contribution

It introduces and studies the properties of compact-bounded and weakly compact-bounded spaces in the context of (para)topological groups, expanding understanding of feebly compact spaces.

Findings

Characterization of compact-bounded spaces in topological groups

Analysis of weakly compact-bounded subsets and their properties

Relationships between feebly compact, compact-bounded, and weakly compact-bounded spaces

Abstract

We will study two subclasses of the class of feebly compact spaces in the class of (para)topological groups, the compact-bounded and weakly compact-bounded spaces, both introduced by J. Angoa, Y. F. Ortiz-Castillo and A. Tamariz-Mascar\'ua in [4]. Also, we will study the $r$-weakly compact-bounded subsets of a topological space $X$.