English

A net theoretic approach to homotopy theory

Algebraic Topology 2024-10-30 v2 General Topology

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.

Keywords

Cite

@article{arxiv.2410.18245,
  title  = {A net theoretic approach to homotopy theory},
  author = {Renan Maneli Mezabarba and Rodrigo Santos Monteiro and Thales Fernando Vilamaior Paiva},
  journal= {arXiv preprint arXiv:2410.18245},
  year   = {2024}
}

Comments

Minor typos corrected in Example 3.6. Remarks 3.7 and 5.1 were added