On setwise betweenness
| Autor: | Qays R. Shakir |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Applied General Topology, Vol 24, Iss 1, Pp 115-123 (2023) |
| Druh dokumentu: | article |
| ISSN: | 1576-9402 1989-4147 |
| DOI: | 10.4995/agt.2023.18061 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|