On setwise betweenness
In this article, we investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of X if every subcontinuum K of X containing bo...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2023-04-01
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| Series: | Applied General Topology |
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| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/18061 |
| _version_ | 1827972292291854336 |
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| author | Qays R. Shakir |
| author_facet | Qays R. Shakir |
| author_sort | Qays R. Shakir |
| collection | DOAJ |
| description | In this article, we investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of X if every subcontinuum K of X containing both a and b intersects C. The notion of an interval [a,b] then arises naturally. Further interesting questions are derived from considering such intervals within an associated hyperspace on X. We explore these ideas within the context of the Vietoris topology and n-symmetric product hyperspaces on all nonempty closed subsets of a topological space X, CL(X). Moreover, an alternative pointwise interval, derived from setwise intervals, is introduced. |
| first_indexed | 2024-04-09T19:20:48Z |
| format | Article |
| id | doaj.art-1ae1fd4f9850494aa910e3680d0aec1d |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-09T19:20:48Z |
| publishDate | 2023-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-1ae1fd4f9850494aa910e3680d0aec1d2023-04-05T11:41:08ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472023-04-0124111512310.4995/agt.2023.1806117251On setwise betweennessQays R. Shakir0https://orcid.org/0000-0002-5022-9212Middle Technical University, IraqIn this article, we investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of X if every subcontinuum K of X containing both a and b intersects C. The notion of an interval [a,b] then arises naturally. Further interesting questions are derived from considering such intervals within an associated hyperspace on X. We explore these ideas within the context of the Vietoris topology and n-symmetric product hyperspaces on all nonempty closed subsets of a topological space X, CL(X). Moreover, an alternative pointwise interval, derived from setwise intervals, is introduced.https://polipapers.upv.es/index.php/AGT/article/view/18061betweenness relationroad systemhyperspace |
| spellingShingle | Qays R. Shakir On setwise betweenness Applied General Topology betweenness relation road system hyperspace |
| title | On setwise betweenness |
| title_full | On setwise betweenness |
| title_fullStr | On setwise betweenness |
| title_full_unstemmed | On setwise betweenness |
| title_short | On setwise betweenness |
| title_sort | on setwise betweenness |
| topic | betweenness relation road system hyperspace |
| url | https://polipapers.upv.es/index.php/AGT/article/view/18061 |
| work_keys_str_mv | AT qaysrshakir onsetwisebetweenness |