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

• Autorzy: Aleš Nekvinda , Ondřej Zindulka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
• 28A78: Hausdorff and packing measures
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 213
• Numer: 3
• Strony: 221-232

Daty

wydano

2011

Twórcy

autor

Aleš Nekvinda

• Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 160 00 Praha 6, Czech Republic

autor

Ondřej Zindulka

• Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 160 00 Praha 6, Czech Republic

Identyfikatory

DOI

10.4064/fm213-3-3