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

Aleš Nekvinda; Ondřej Zindulka

Fundamenta Mathematicae (2011)

- Volume: 213, Issue: 3, page 221-232
- ISSN: 0016-2736

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topAleš 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 -

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