A net theoretic approach to homotopy theory

TL;DR

This paper introduces a net-theoretic framework for convergence spaces to simplify continuous convergence descriptions, enabling advanced homotopy analysis and a generalized Seifert-van Kampen theorem for limit spaces.

Contribution

It develops a net-theoretic approach to convergence spaces, facilitating homotopy theory applications and extending classical theorems to limit spaces.

Findings

Defined fundamental groupoids for limit spaces

Proved a generalized Seifert-van Kampen theorem

Simplified continuous convergence descriptions

Abstract

This paper uses a net-theoretic approach to convergence spaces, aimed to simplify the description of continuous convergence in order to apply it in problems concerning Homotopy Theory. We present methods for handling homotopies of limit spaces, define fundamental groupoids, and prove a generalized version of the Seifert-van Kampen Theorem for limit spaces.