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 bo...
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| 格式: | Artículo |
| 语言: | English |
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2020
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| 在线阅读: | http://www.sciencedirect.com/science/article/pii/S0022404919303238 |
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| 总结: | 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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