Acquiring a dimension: from topology to convergence theory

TL;DR

This paper introduces convergence theory as an extension of topology that is closed under key operations like exponentiation, aiming to increase its visibility and understanding within the mathematical community.

Contribution

It presents convergence theory as a valuable extension of topology, highlighting its properties and potential for broader adoption in mathematics.

Findings

Convergence theory extends general topology.

It is closed under operations like exponentiation.

The paper aims to promote awareness of convergence theory.

Abstract

Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, convergence theory remains rather unknown. It is an aim of this paper to make it more familiar to the mathematical community.