Let M be a subset of a metric space M. A connected component of A is a maximal connected subset of A. That is, a set C is a connected component of A if it satisfies: (a) CCA. (b) C is connected. (c) IF D is connected and C C DC A, then D = C. Maximal connected components exist, in fact every point of A is contained in a maximal connected component of A. We simply define for pЄ A Cp={CC is connected, p = CCA} The family of all connected sets components containing p is not empty;

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