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Preliminaries

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2032)

Abstract

In this chapter we will state some of the most important results on finite spaces which are previous to our work. These results can be summarized by the following three items: 1. The correspondence between finite topological spaces and finite partially ordered sets, first considered by Alexandroff in [1] in 1937. The combinatorial description of homotopy types of finite spaces, discovered by Stong in his beautiful article [76] of 1966. 3. The connection between finite spaces and polyhedra, found by McCord [55] also in 1966.

Keywords

  • Topological Space
  • Simplicial Complex
  • Homotopy Type
  • Hasse Diagram
  • Homotopy Equivalent

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2011 Springer-Verlag Berlin Heidelberg

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Barmak, J.A. (2011). Preliminaries. 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_1

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