A Cantor set in the plane that is not $sigma$-monotone

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F11%3A00187540" target="_blank" >RIV/68407700:21110/11:00187540 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

A Cantor set in the plane that is not $sigma$-monotone

Original language description

A metric space $(X,d)$ is \emph{monotone} if there is a linear order $<$ on $X$ and a constant $c$ such that $d(x,y)\leq c\,d(x,z)$ for all $x<y<z$ in $X$, and \si monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not \si monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not \si monotone.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2011

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

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Volume of the periodical

213

Issue of the periodical within the volume

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Country of publishing house

PL - POLAND

Number of pages

12

Pages from-to

221-232

UT code for WoS article

000296298400003

EID of the result in the Scopus database

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