Geodesic
A category to classify compact Hausdorff spaces and finite spaces
Homology, homotopy, and applications, Tome 27 (2025) no. 1, pp. 17-28.

Voir la notice de l'article provenant de la source International Press of Boston

We construct a category that classifies compact Hausdorff spaces by their shape and finite topological spaces by their weak homotopy type. This construction is based on inverse systems of finite covers, that are considered as finite partially ordered sets.
DOI : 10.4310/HHA.2025.v27.n1.a2
Classification : |55P55, | 54C56, | 06A06, | 54C56, | 18Fxx
Keywords: finite topological space, poset, compact Hausdorff space, shape theory, weak homotopy type 
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     title = {A category to classify compact {Hausdorff} spaces and finite spaces},
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Pedro J. Chocano; Manuel A. Morón; Francisco R. Ruiz del Portal. A category to classify compact Hausdorff spaces and finite spaces. Homology, homotopy, and applications, Tome 27 (2025) no. 1, pp. 17-28. doi : 10.4310/HHA.2025.v27.n1.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2025.v27.n1.a2/

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