On the Hahn--Mazurkiewicz theorem
- Cite this article as:
- Bognár, M. Acta Mathematica Hungarica (2004) 102: 37. doi:10.1023/B:AMHU.0000023208.49494.96
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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.