The Frame of Nuclei on an Alexandroff Space
Let O be the frame of open sets of a topological space S, and let (O ) be the frame of nuclei on O . For an Alexandroff space S, we prove that (O ) is spatial iff the infinite binary tree 2 does not embed isomorphically into (S,≤), where ≤ is the specialization preorder of S.
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | México |
| Institución: | Universidad Autónoma de Ciudad Juárez |
| Repositorio: | Repositorio Institucional de la Universidad Autónoma de Ciudad Juárez |
| OAI Identifier: | oai:uacj.mx:oai:cathi.uacj.mx:20.500.11961ir-15652 |
| Acceso en línea: | https://link.springer.com/article/10.1007/s11083-020-09528-1 |
| Access Level: | acceso abierto |
| Palabra clave: | Frame Locale Nucleus Priestley space Alexandroff space Partial order Total order Tree info:eu-repo/classification/cti/1 |
| Sumario: | Let O be the frame of open sets of a topological space S, and let (O ) be the frame of nuclei on O . For an Alexandroff space S, we prove that (O ) is spatial iff the infinite binary tree 2 does not embed isomorphically into (S,≤), where ≤ is the specialization preorder of S. |
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