The betweenness relation distinguishes non-similar pairs of concentric circles
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00639753" target="_blank" >RIV/67985840:_____/25:00639753 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00025-025-02514-2" target="_blank" >https://doi.org/10.1007/s00025-025-02514-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-025-02514-2" target="_blank" >10.1007/s00025-025-02514-2</a>
Alternative languages
Result language
angličtina
Original language name
The betweenness relation distinguishes non-similar pairs of concentric circles
Original language description
Two subsets A, B of the plane are betweenness isomorphic if there is a bijection f:A→B such that, for every x,y,z∈A, the point f(z) lies on the line segment connecting f(x) and f(y) if and only if z lies on the line segment connecting x and y. In general, it is quite difficult to tell whether two given subsets of the plane are betweenness isomorphic. We concentrate on the case when the sets A, B belong to the family Ac of unions of pairs of concentric circles in the plane. We prove that A,B∈Ac are betweenness isomorphic if and only if they are similar. In particular, there are continuum many betweenness isomorphism classes in Ac, and each of these classes consists exactly of all scaled translations of an arbitrary representative of the class. Furthermore, we show that every betweenness isomorphism between sets A,B∈Ac is exactly the restriction of a scaled isometry of the plane.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GX20-31529X" target="_blank" >GX20-31529X: Abstract convergence schemes and their complexities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Results in Mathematics
ISSN
1422-6383
e-ISSN
1420-9012
Volume of the periodical
80
Issue of the periodical within the volume
7
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
196
UT code for WoS article
001567833300002
EID of the result in the Scopus database
2-s2.0-105015425285