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

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Authors and Affiliations

  1. Department of Analysis, Eötvös Loránd University, 1117, Budapest, Pázmány P. sétány 1/C, Hungary

    Mátyás Bognár

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  1. Mátyás Bognár
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Bognár, M. On the Hahn--Mazurkiewicz theorem. Acta Mathematica Hungarica 102, 37–84 (2004). https://doi.org/10.1023/B:AMHU.0000023208.49494.96

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  • DOI: https://doi.org/10.1023/B:AMHU.0000023208.49494.96

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