A Cantor set in the plane that is not σ-monotone

Aleš Nekvinda, and Ondřej Zindulka. "A Cantor set in the plane that is not σ-monotone." Fundamenta Mathematicae 213.3 (2011): 221-232. <http://eudml.org/doc/283055>.

@article{AlešNekvinda2011,
abstract = {A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.},
author = {Aleš Nekvinda, Ondřej Zindulka},
journal = {Fundamenta Mathematicae},
keywords = {monotone metric space; Cantor set; Hausdorff measure; Hausdorff dimension},
language = {eng},
number = {3},
pages = {221-232},
title = {A Cantor set in the plane that is not σ-monotone},
url = {http://eudml.org/doc/283055},
volume = {213},
year = {2011},
}

TY - JOUR
AU - Aleš Nekvinda
AU - Ondřej Zindulka
TI - A Cantor set in the plane that is not σ-monotone
JO - Fundamenta Mathematicae
PY - 2011
VL - 213
IS - 3
SP - 221
EP - 232
AB - A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.
LA - eng
KW - monotone metric space; Cantor set; Hausdorff measure; Hausdorff dimension
UR - http://eudml.org/doc/283055
ER -