Algebraic topology of finite topological spaces

Authors

Keywords:

finite topological spaces, partially ordered sets (posets), Hasse diagrams, homotopy theory, minimal spaces, simplicial complexes.

Abstract

This work follows R. Stong and M. McCord’s study lines on finite topological spaces. Although they are two different approaches, they intersect at one point: posets. On the one hand, we will classify finite topological spaces through posets, according to Stong’s Classification Theorem. On the other hand, following McCord’s Theorem, we will examine how posets encode the homotopic information of both polyhedra and finite topological spaces. We will conclude by providing a finite model of a compact connected surface.

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How to Cite

Subirà Cribillers, M. (2024). Algebraic topology of finite topological spaces. Reports@SCM, 9(1), 41–52. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154340

Issue

Vol. 9 No. 1 (2024)

Section

Articles

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