Statistical Compactness

TL;DR

This paper introduces statistical compactness, a new variant of compactness based on statistical convergence, and explores its properties including a form of one-point statistical compactification.

Contribution

It develops the concept of statistical compactness and investigates one-point statistical compactification, expanding the theoretical framework of compactness using statistical convergence.

Findings

Introduces statistical compactness as a new theoretical concept.

Studies one-point statistical compactification.

Extends the theory of compactness with statistical convergence.

Abstract

Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one point statistical compactification is studied to some extent too.