Geodesic
On typical parametrizations of finite-dimensional compacta on the Cantor set
Paweł Milewski 1
1 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland
Fundamenta Mathematicae, Tome 174 (2002) no. 3, pp. 253-261 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm174-3-5
Keywords: prove perfect finite dimensional compactum almost every continuous surjection cantor set set points maximal order uncountable moreover perfect compactum positive finite dimension typical parametrization cantor set set points maximal order homeomorphic product rationals cantor set

Paweł Milewski  1

1 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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Paweł Milewski. On typical parametrizations of finite-dimensional compacta
 on the Cantor set. Fundamenta Mathematicae, Tome 174 (2002) no. 3, pp. 253-261. doi: 10.4064/fm174-3-5

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