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math.AT2024
Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces
Rodrigo Santos Monteiro
Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of expo…
math.AT2024
Pasting and stability in convergence spaces
Renan Maneli Mezabarba, Rodrigo Santos Monteiro, Thales Fernando Vilamaior Paiva
We prove a pasting lemma for locally finite closed covers of convergence spaces with limit codomains. We also show how the validity of such lemmas characterizes limit spaces.