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Finite topological spaces. (English) Zbl 1167.55300

Summary: We show that the study of topological \(T_0\)-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be \(T_0\).

MSC:

55M05 Duality in algebraic topology
55N30 Sheaf cohomology in algebraic topology
06A99 Ordered sets
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