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Results tagged with locales
Search options questions only
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user 17064
Questions taking place in the category of locales, which is given by the opposite of the category of frames. Also appropriate for questions about pointless topology.
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Concrete description of “DeMorganian” open sets
Let me begin with a few definitions. My question will be basically how to simplify them to something more manageable. The motivation for these definitions is given at the end.
Let $X$ be a topologic …
- 32.5k
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votes
1
answer
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Preimage of a sublocale by a morphism of locales: description by nucleus?
The category of locales is the opposite of the category of frames: we write $\mathcal{O}(X)$ for the frame associated to a locale $X$ and we call it its “frame of opens”. … If $f\colon X \to Y$ is a morphism of locales, and $S \subseteq \mathcal{O}(Y)$ a sublocale of $Y$, we define the preimage of $S$ by $f$ [see: Picado & Pultr, Frames and Locales, III.4.2] to be the smallest …
- 32.5k
3
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answer
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Computing the Heyting operation on the frame of nuclei
(The following definitions are meant to be standard and are reproduced for completeness of the question.) A frame is a partially ordered set in which every finite subset has a greatest lower bound (“ …
- 32.5k
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What is known about sublocales defined by regular nuclei?
what to call such sublocales (the word “regular” isn't good because “regular locale” means something different and “regular sublocale” should probably be reserved for sublocales that, when viewed as locales …
- 32.5k