On joins of complemented sublocales (Preprint)
| <Reference List> | |
| Type: | Preprint |
| National /International: | International |
| Title: | On joins of complemented sublocales |
| Publication Date: | 2020-07-30 |
| Authors: |
- Igor Arrieta Torres
|
| Abstract: | The system Sc(L) consisting of joins of closed sublocales of a locale L is known to be a frame, and for L subfit it coincides with the Booleanization Sb(L) of the coframe of sublocales of L. In this paper, we study Sb(L) for a general locale L. We show that Sc(L) is always a subframe of Sb(L). Moreover, if X is a TD-space, we prove that Sb(Ω(X)) is precisely the set of classical subspaces of X, and that a locale L is TD-spatial iff the Boolean algebra Sb(L) is atomic. Some functoriality properties of Sb(L) are also studied. |
| Institution: | DMUC 20-23 |
| Online version: | http://www.mat.uc.pt...prints/eng_2020.html |
| Download: | Not available |
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