Convex geometries yielded by transit functions
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 sub...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AGH Univeristy of Science and Technology Press
2025-07-01
|
| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol45/4/art/opuscula_math_4520.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849318396256059392 |
|---|---|
| author | Manoj Changat Lekshmi Kamal K. Sheela Iztok Peterin Ameera Vaheeda Shanavas |
| author_facet | Manoj Changat Lekshmi Kamal K. Sheela Iztok Peterin Ameera Vaheeda Shanavas |
| author_sort | Manoj Changat |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8eaa7830940e4cd7bd64f8a7f9859f2c |
| institution | Kabale University |
| issn | 1232-9274 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj-art-8eaa7830940e4cd7bd64f8a7f9859f2c2025-08-20T03:50:49ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742025-07-01454423450https://doi.org/10.7494/OpMath.2025.45.4.4234520Convex geometries yielded by transit functionsManoj Changat0https://orcid.org/0000-0001-7257-6031Lekshmi Kamal K. Sheela1https://orcid.org/0000-0002-8527-3280Iztok Peterin2https://orcid.org/0000-0002-1990-6967Ameera Vaheeda Shanavas3University of Kerala, Department of Futures Studies, Thiruvananthapuram - 695581, IndiaUniversity of Kerala, Department of Futures Studies, Thiruvananthapuram - 695581, IndiaFaculty of Electrical Engineering and Computer Science, University of Maribor, Koroška 46, 2000 Maribor, SloveniaUniversity of Kerala, Department of Futures Studies, Thiruvananthapuram - 695581, IndiaLet \(V\) 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.https://www.opuscula.agh.edu.pl/vol45/4/art/opuscula_math_4520.pdfminkowski-krein-milman propertyconvexityconvex geometrytransit function |
| spellingShingle | Manoj Changat Lekshmi Kamal K. Sheela Iztok Peterin Ameera Vaheeda Shanavas Convex geometries yielded by transit functions Opuscula Mathematica minkowski-krein-milman property convexity convex geometry transit function |
| title | Convex geometries yielded by transit functions |
| title_full | Convex geometries yielded by transit functions |
| title_fullStr | Convex geometries yielded by transit functions |
| title_full_unstemmed | Convex geometries yielded by transit functions |
| title_short | Convex geometries yielded by transit functions |
| title_sort | convex geometries yielded by transit functions |
| topic | minkowski-krein-milman property convexity convex geometry transit function |
| url | https://www.opuscula.agh.edu.pl/vol45/4/art/opuscula_math_4520.pdf |
| work_keys_str_mv | AT manojchangat convexgeometriesyieldedbytransitfunctions AT lekshmikamalksheela convexgeometriesyieldedbytransitfunctions AT iztokpeterin convexgeometriesyieldedbytransitfunctions AT ameeravaheedashanavas convexgeometriesyieldedbytransitfunctions |