The Hausdorff – Alexandroff Theorem and its Application in Theory of Curves
نویسنده
چکیده
Eighty years ago, Felix Hausdorff and Paul Alexandroff published independently a theorem asserting that every compact metric space is a continuous image of the Cantor set. This theorem found its application in various branches of mathematics and played also an important role in the theory of curves. The complete characterization of continuous interval images (i.e. Jordan curves) given by the Hahn – Mazurkiewicz theorem can be shown as a simple consequence of a few statements, including the Hausdorff – Alexandroff theorem.
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