On typical parametrizations of finite-dimensional compacta on the Cantor set
Volume 174 / 2002
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.
