Topology

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

Chapter Chapter 3 in A Comprehensive Textbook on Metric Spaces, 2023, pp 63-88 from Springer

Abstract: Abstract Consider the graphs of the capital letters of the English alphabet in a plane. By stretching and twisting, one can deform U onto S and vice versa. But can you obtain P and S from each other by twisting and stretching only? Topology deals with such questions about continuous deformations. In Sect. 9.2, the notion of homeomorphisms will further reflect upon this idea. In this chapter, we present a detailed discussion on the basic topological notions such as open sets, closed sets, limits points, closures, and boundaries. It contains a section on continuity in metric spaces, which includes the case of Euclidean spaces and the relationship of continuity and uniform convergence. Little sections on subspace topology and topology of normed linear spaces are also included.

Date: 2023
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DOI: 10.1007/978-981-99-2738-8_3

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