On typical parametrizations of finite-dimensional compacta on the Cantor set

Volume 174 / 2002

Paweł Milewski Fundamenta Mathematicae 174 (2002), 253-261 MSC: 54D30, 54C50. DOI: 10.4064/fm174-3-5

Abstract

We prove that if $X$ is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto $X$, the set of points of maximal order is uncountable. Moreover, if $X$ is a perfect compactum of positive finite dimension then for a typical parametrization of $X$ on the Cantor set, the set of points of maximal order is homeomorphic to the product of the rationals and the Cantor set.

Authors

  • Paweł MilewskiInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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