Abstract
In Sect. 3.3 we proved that in general, if K is a finite simplicial complex, there is no finite space with the homotopy type of |K|. However, by Theorem 2.4.12 any compact polyhedron is weak homotopy equivalent to a finite space. In this chapter we will study finite models of polyhedra in this sense and we will describe the minimal finite models of some well-known (Hausdorff) spaces, i.e. weak homotopy equivalent finite spaces of minimum cardinality. The main results of this chapter appear in [7].
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© 2011 Springer-Verlag Berlin Heidelberg
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Barmak, J.A. (2011). Minimal Finite Models. In: Algebraic Topology of Finite Topological Spaces and Applications. Lecture Notes in Mathematics(), vol 2032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22003-6_3
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DOI: https://doi.org/10.1007/978-3-642-22003-6_3
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22002-9
Online ISBN: 978-3-642-22003-6
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