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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX20-31529X" target="_blank" >GX20-31529X: Abstraktní konvergenční schémata a jejich složitost</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Advances in Geometry

ISSN

1615-715X

e-ISSN

1615-7168

Svazek periodika

24

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

20

Strana od-do

473-492

Kód UT WoS článku

001339249500010

EID výsledku v databázi Scopus

2-s2.0-85207806092