Abstract
By a continuum we usually mean a metric (or Hausdorff) compact connected space. The original definition of 1883, due to Georg Cantor, [126], p. 576, stated that a subset of a Euclidean space is a continuum provided it is perfect (i.e. closed and dense-in-itself, or — equivalently — coincides with its first derivative) and connected, i.e. if for every two of its points a and b and for each positive number є there corresponds a finite system of points a = p 0, p 1, ..., p n = b such that the distance between any two consecutive points of the system is less than є. The equivalence of the two definitions for compact metric spaces is shown e.g. in Kuratowski’s monograph [390], vol. 2, §47, I, Theorem 0, p. 167.
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Charatonik, J.J. (1998). History of Continuum Theory. In: Aull, C.E., Lowen, R. (eds) Handbook of the History of General Topology. History of Topology, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1756-4_11
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