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

Paweł Milewski. "On typical parametrizations of finite-dimensional compacta on the Cantor set." Fundamenta Mathematicae 174.3 (2002): 253-261. <http://eudml.org/doc/282904>.

@article{PawełMilewski2002,
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.},
author = {Paweł Milewski},
journal = {Fundamenta Mathematicae},
keywords = {dimension; compact; parametrization; residual},
language = {eng},
number = {3},
pages = {253-261},
title = {On typical parametrizations of finite-dimensional compacta on the Cantor set},
url = {http://eudml.org/doc/282904},
volume = {174},
year = {2002},
}

TY - JOUR
AU - Paweł Milewski
TI - On typical parametrizations of finite-dimensional compacta on the Cantor set
JO - Fundamenta Mathematicae
PY - 2002
VL - 174
IS - 3
SP - 253
EP - 261
AB - 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.
LA - eng
KW - dimension; compact; parametrization; residual
UR - http://eudml.org/doc/282904
ER -