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When is the frame of nuclei spatial: A new approach
- Publication Year :
- 2019
-
Abstract
- For a frame $L$, let $X_L$ be the Esakia space of $L$. We identify a special subset $Y_L$ of $X_L$ consisting of nuclear points of $X_L$, and prove the following results: $L$ is spatial iff $Y_L$ is dense in $X_L$. If $L$ is spatial, then $N(L)$ is spatial iff $Y_L$ is weakly scattered. If $L$ is spatial, then $N(L)$ is boolean iff $Y_L$ is scattered. As a consequence, we derive the well-known results of Beazer and Macnab [1979], Simmons [1980], Niefield and Rosenthal [1987], and Isbell [1972].
- Subjects :
- Mathematics - General Topology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1906.03636
- Document Type :
- Working Paper