Homeomorphisms

Surinder Pal Singh Kainth ()
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Surinder Pal Singh Kainth: Panjab University, Department of Mathematics

Chapter Chapter 9 in A Comprehensive Textbook on Metric Spaces, 2023, pp 243-277 from Springer

Abstract: Abstract Homeomorphisms are essentially topological isomorphisms. In other words, homeomorphic spaces are same from the topological viewpoint. In Sect. 4.4, we have already discussed isometries, as a particular class of homeomorphisms. A general discussion on homeomorphisms begins in Sect. 9.2. Until that we strive on some of its particular cases given by topologically, uniformly, and Lipschitz equivalent metrics. The third section of this chapter provides several extension theorems, including the results by Tietze, Kuratowski, and Lavrentiev. Finally, we present the case of normed spaces, particularly the equivalence of all norms on finite-dimensional spaces.

Date: 2023
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DOI: 10.1007/978-981-99-2738-8_9

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