Part of the book series:Compact Textbooks in Mathematics ((CTM))
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Abstract
In this section, we introduce the concept of compactness of topological spaces. After that, we discuss a relative version of this notion, that of a proper map. A technical section about Tychonoff’s theorem follows, which can be skipped at the first reading. We then turn to mapping spaces. As it is mainly the function spaces that are of interest in analysis, in topology, it is the spaces of continuous maps that provide extremely important examples of topological spaces.
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References
Groves, J. (2012). An elementary counterexample in the compact-open topology.The American Mathematical Monthly,119, 693–694.
McCord, M. C. (1969). Classifying spaces and infinite symmetric products.Transactions of the American Mathematical Society,146, 273–298.
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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). Compactness and Mapping Spaces. In: A Basic Course in Topology. Compact Textbooks in Mathematics. Birkhäuser, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-70602-2_4
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