Oriented components and their separations
There is a tight connection between connectedness, connected components, and certain types of separation spaces. Recently, axiom systems for oriented connectedness were proposed leading to the notion of reaches. Here, we introduce production relations as a further generalization of connectivity spac...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2017-10-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/5868 |
| _version_ | 1818684986556940288 |
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| author | Baerbel M R Stadler Peter F. Stadler |
| author_facet | Baerbel M R Stadler Peter F. Stadler |
| author_sort | Baerbel M R Stadler |
| collection | DOAJ |
| description | There is a tight connection between connectedness, connected components, and certain types of separation spaces. Recently, axiom systems for oriented connectedness were proposed leading to the notion of reaches. Here, we introduce production relations as a further generalization of connectivity spaces and reaches and derive associated systems of oriented components that generalize connected components in a natural manner. The main result is a characterization of generalized reaches in terms of equivalent separation spaces. |
| first_indexed | 2024-12-17T10:59:21Z |
| format | Article |
| id | doaj.art-c63266fcc531422499b031137310a901 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-17T10:59:21Z |
| publishDate | 2017-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-c63266fcc531422499b031137310a9012022-12-21T21:51:45ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472017-10-0118225527510.4995/agt.2017.58686089Oriented components and their separationsBaerbel M R Stadler0Peter F. Stadler1Max Planck Institute for Mathematics in the SciencesLeipzig UniversityThere is a tight connection between connectedness, connected components, and certain types of separation spaces. Recently, axiom systems for oriented connectedness were proposed leading to the notion of reaches. Here, we introduce production relations as a further generalization of connectivity spaces and reaches and derive associated systems of oriented components that generalize connected components in a natural manner. The main result is a characterization of generalized reaches in terms of equivalent separation spaces.https://polipapers.upv.es/index.php/AGT/article/view/5868separation spacespre-proximitiesgeneralized topological spaces. |
| spellingShingle | Baerbel M R Stadler Peter F. Stadler Oriented components and their separations Applied General Topology separation spaces pre-proximities generalized topological spaces. |
| title | Oriented components and their separations |
| title_full | Oriented components and their separations |
| title_fullStr | Oriented components and their separations |
| title_full_unstemmed | Oriented components and their separations |
| title_short | Oriented components and their separations |
| title_sort | oriented components and their separations |
| topic | separation spaces pre-proximities generalized topological spaces. |
| url | https://polipapers.upv.es/index.php/AGT/article/view/5868 |
| work_keys_str_mv | AT baerbelmrstadler orientedcomponentsandtheirseparations AT peterfstadler orientedcomponentsandtheirseparations |