, Volume 102, Issue 1-2, pp 37-84

On the Hahn--Mazurkiewicz theorem

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Abstract

The following generalization of the Hahn-Mazurkiewicz theorem is proved: Let (E,e) be a locally compact locally connected metric space. Let M be a continuum in this space and let d,e∈ M. Then there is a continuous mapping f: [0,1]→E such that f(0) = d, f(1)= e and Mf([0,1]). Also some corollaries of this theorem are proved.