A net theoretic approach to homotopy theory

2024/10/23 by Mezabarba, Renan Maneli, Monteiro, Rodrigo Santos, Paiva, Thales Fernando Vilamaior · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2410.18245

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.

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