@Article{Changat2025,
author = "Changat, Manoj and Sheela, Lekshmi Kamal K. and Peterin, Iztok and Shanavas, Ameera Vaheeda",
title = "Convex geometries yielded by transit functions",
journal = "Opuscula Math.",
year = "2025",
volume = "45",
number = "4",
pages = "423--450",
doi = "https://doi.org/10.7494/OpMath.2025.45.4.423",
url = "https://doi.org/10.7494/OpMath.2025.45.4.423",
abstract = "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.",
keywords = "Minkowski-Krein-Milman property, convexity, convex geometry, transit function",
issn = "1232-9274"
}