Connectedness

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

Chapter Chapter 6 in A Comprehensive Textbook on Metric Spaces, 2023, pp 155-181 from Springer

Abstract: Abstract The notion of path connectedness is more intuitive than connectedness. It appears before connectedness, even in history. Motivated by that, we start this chapter with path connectedness and its relationship with continuity; through which we deduce the Intermediate Value Theorem. Then we discuss connectedness and its characterizations, followed by a section on components; which provides insights into connected components and path components. Finally, we present some miscellaneous topics such as local connectedness, quasi-components, and totally disconnected spaces.

Date: 2023
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DOI: 10.1007/978-981-99-2738-8_6

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