Betweenness isomorphism classes of circles with finitely many points inside
Martin Dole\v{z}al, Jan Kol\'a\v{r}, Janusz Morawiec
TL;DR
This paper characterizes when two circles with finitely many interior points are betweenness isomorphic, providing a complete classification for circles with three collinear interior points.
Contribution
It offers a necessary and sufficient condition for betweenness isomorphism of such circles and fully characterizes classes with three collinear interior points.
Findings
Established a criterion for betweenness isomorphism between circles with interior points.
Provided a complete classification for circles with three collinear interior points.
Enhanced understanding of geometric betweenness structures.
Abstract
We give a necessary and sufficient condition for two circles, each with finitely many points added inside, to be betweenness isomorphic. We fully characterize the betweenness isomorphism classes in the family consisting of all circles with three collinear points inside.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Finite Group Theory Research