TY  - JOUR
ID  - Changat2025
LB  - Changat2025
AU  - Changat, Manoj
AU  - Sheela, Lekshmi Kamal K.
AU  - Peterin, Iztok
AU  - Shanavas, Ameera Vaheeda
TI  - Convex geometries yielded by transit functions
ST  - Convex geometries yielded by transit functions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 4
SP  - 423
EP  - 450
DO  - https://doi.org/10.7494/OpMath.2025.45.4.423
UR  - https://doi.org/10.7494/OpMath.2025.45.4.423
AB  - Let \(V\) be a finite nonempty set. A transit function is a map \(R:V\times V\rightarrow 2^V\) such that \(R(u,u)=\{u\}\), \(R(u,v)=R(v,u)\) and \(u\in R(u,v)\) holds for every \(u,v\in V\). A set \(K\subseteq V\) is \(R\)-convex if \(R(u,v)\subset K\) for every \(u,v\in K\) and all \(R\)-convex subsets of \(V\) form a convexity \(\mathcal{C}_R\). We consider the Minkowski-Krein-Milman property that every \(R\)-convex set \(K\) in a convexity \(\mathcal{C}_R\) is the convex hull of the set of extreme points of \(K\) from axiomatic point of view and present a characterization of it. Later we consider several well-known transit functions on graphs and present the use of the mentioned characterizations on them.
KW  - Minkowski-Krein-Milman property
KW  - convexity
KW  - convex geometry
KW  - transit function
SN  - 1232-9274
ER  -