Acta Mathematica Hungarica

, Volume 102, Issue 1, pp 37-84

First online:

On the Hahn--Mazurkiewicz theorem

  • Mátyás BognárAffiliated withDepartment of Analysis, Eötvös Loránd University

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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 M⊂f([0,1]). Also some corollaries of this theorem are proved.

connected space locally locally compact space continuous mappings