When is the frame of nuclei spatial: A new approach
For a frame L, let XL be the Esakia space of L. We identify a special subset YL of XL consisting of nuclear points of XL, and prove the following results: • L is spatial iff YL is dense in XL. • If L is spatial, then N(L) is spatial iff YL is weakly scattered. • If L is spatial, then N(L) is boolean...
| 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-15657 |
| Acceso en línea: | http://www.sciencedirect.com/science/article/pii/S0022404919303238 |
| Access Level: | acceso abierto |
| Palabra clave: | Frame Nucleus Spatial frame Boolean frame Priestley space Scattered space info:eu-repo/classification/cti/1 |
| Sumario: | For a frame L, let XL be the Esakia space of L. We identify a special subset YL of XL consisting of nuclear points of XL, and prove the following results: • L is spatial iff YL is dense in XL. • If L is spatial, then N(L) is spatial iff YL is weakly scattered. • If L is spatial, then N(L) is boolean iff YL is scattered. As a consequence, we derive the well-known results of Beazer and Macnab [1], Simmons [22], Niefield and Rosenthal [13], and Isbell [10]. |
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