Betweenness isomorphisms in the plane - The case of a circle and points

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00600582" target="_blank" >RIV/67985840:_____/24:00600582 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1515/advgeom-2024-0027" target="_blank" >https://doi.org/10.1515/advgeom-2024-0027</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/advgeom-2024-0027" target="_blank" >10.1515/advgeom-2024-0027</a>

Result language
angličtina
Original language name
Betweenness isomorphisms in the plane - The case of a circle and points
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 each of the sets A, B is of the form C ∪ D where C is a circle and D is a finite set. We fully characterize the betweenness isomorphism classes in the family of all circles with three collinear points inside. In particular, we show that there are only countably many isomorphism classes, for which we provide an algebraic description.
Czech name
—
Czech description
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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

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

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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