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A net theoretic approach to homotopy theory

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arxiv 2410.18245 v2 pith:UJMKIB5T submitted 2024-10-23 math.AT math.GN

Renan Maneli Mezabarba , Rodrigo Santos Monteiro , Thales Fernando Vilamaior Paiva This is my paper · ORCID
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keywords spacesapproachconvergencehomotopylimittheoryaimedapply
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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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  1. Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces

    math.AT 2024-12 conditional novelty 4.0 of 10

    A net-based construction of the fundamental groupoid and a groupoid Seifert-van Kampen theorem for limit spaces.

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