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Abstract
Simplicial sets are discrete, combinatorial models for topological spaces that simplify the construction of many objects in topology. It turns out that the homotopy theory of simplicial sets is equivalent to that of topological spaces. The importance of simplicial sets for topology is based on the fact that many objects in topology are constructed as realisations of simplicial sets. Some perspectives on this will be given at the end of this chapter.
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References
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Goerss, P., & Jardine, J. F. (1999).Simplicial homotopy theory.Progress in mathematics (Vol. 174). Birkhäuser Verlag.
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Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany
Gerd Laures
School of Mathematical and Physical Sciences, University of Sheffield, Sheffield, UK
Markus Szymik
- Gerd Laures
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- Markus Szymik
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Laures, G., Szymik, M. (2025). Simplicial Sets. In: A Basic Course in Topology. Compact Textbooks in Mathematics. Birkhäuser, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-70602-2_11
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