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Rational Homotopy in Pseudotopological Spaces
Jonathan Treviño-Marroquín
Pseudotopological spaces are the Cartesian closed hull of the category of Čech closure spaces. In this paper, we give a direct proof that the model category of the pseudotopologica…
Graphs and Their Clique Complexes Are Pseudotopological Weakly Homotopy Equivalent
Jonathan Treviño-Marroquín
We establish a connection between the graphs and their geometric realizations of their clique complexes, proving that graphs with their canonical pseudotopological structure, are w…
Semi-coarse Spaces: Fundamental Groupoid and the van Kampen Theorem
Jonathan Treviño-Marroquín
In algebraic topology, the fundamental groupoid is a classical homotopy invariant which is defined using continuous maps from the closed interval to a topological space. In this pa…
Semi-coarse Spaces, Homotopy and Homology
Antonio Rieser, Jonathan Treviño-Marroquín
We begin the study the algebraic topology of semi-coarse spaces, which are generalizations of coarse spaces that enable one to endow non-trivial `coarse-like' structures to compact…