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Basic Concepts of Topology

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A Basic Course in Topology

Part of the book series: Compact Textbooks in Mathematics ((CTM))

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Topology is the branch of mathematics dedicated to the study of continuous maps. The concept of a continuous map has already proven important in calculus, for example, when studying maps between metric spaces compatible with the formation of limits. In this chapter, we will start by reviewing this context and then follow on.

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References

  1. Erné, M. (1974). Struktur- und Anzahlformeln für Topologien auf endlichen Mengen. Manuscripta Mathematica, 11, 221–259.

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  3. Stong, R. E. (1966). Finite topological spaces. Transactions of the American Mathematical Society, 123, 325–340.

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  4. von Querenburg, B. (1979). Mengentheoretische Topologie. Springer-Verlag.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany

    Gerd Laures

  2. School of Mathematical and Physical Sciences, University of Sheffield, Sheffield, UK

    Markus Szymik

Authors
  1. Gerd Laures
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  2. Markus Szymik
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Laures, G., Szymik, M. (2025). Basic Concepts of Topology. In: A Basic Course in Topology. Compact Textbooks in Mathematics. Birkhäuser, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-70602-2_1

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