Abstract
Basically, the notion of connectedness is very easy to grasp. In ℝ2, the set is not. There are various ways to translate this idea into mathematical terms. In this chapter, we discuss two of them. The first is the one to which mathematical usage has reserved the term “connectedness” the second is the “path connectedness” we have already mentioned in Chapter 4. Connectedness (in the strict sense) is the more basic of the two; its definition goes back directly to the notion of a topological space. Path connectedness is intuitively more accessible but less elementary; it relies on properties of the real-number system.
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References
Rotman, Joseph J., An Introduction to Algebraic Topology, Springer-Verlag, New York, 1988.
Greenberg, M. and J.R. Harper, Algebraic Topology: A First Course, Benjamin Cummings, Reading (Mass.), 1981.
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© 1997 Springer Science+Business Media New York
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Buskes, G., van Rooij, A. (1997). Connectedness. In: Topological Spaces. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0665-1_16
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DOI: https://doi.org/10.1007/978-1-4612-0665-1_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6862-8
Online ISBN: 978-1-4612-0665-1
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