| Title: | Convex geometries yielded by transit functions |
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| Authors: | ID Changat, Manoj (Author)
ID Sheela, Lekshmi Kamal K. (Author)
ID Peterin, Iztok (Author)
ID Shanavas, Ameera Vaheeda (Author) |
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| Files: |  PDF - Presentation file, download (721,77 KB)
MD5: 0FFF2E5AC67755E1B80382848FD2C87F
 URL - Source URL, visit https://www.opuscula.agh.edu.pl/om-vol45iss4art1
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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. |
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| Keywords: | Minkowski-Krein-Milman property, convexity, convex geometry, transit function |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 423-450 |
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| Numbering: | Vol. 45, no. 4 |
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| PID: | 20.500.12556/DiRROS-23030  |
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| UDC: | 514:519.17 |
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| ISSN on article: | 1232-9274 |
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| DOI: | 10.7494/OpMath.2025.45.4.423 |
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| COBISS.SI-ID: | 242921987 |
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| Note: |
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| Publication date in DiRROS: | 17.07.2025 |
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| Views: | 327 |
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| Downloads: | 215 |
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