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Results tagged with locales
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user 12705
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.
16
votes
Accepted
Is it possible to completely embed complete Heyting algebras into upsets of a poset?
No, not in general: for instance, the real interval $([0,1],{\le})$, or any non-atomic complete Boolean algebra, does not have such an embedding. This follows from the following characterization:
Pro …
- 47.1k
12
votes
Accepted
Embedding a Brouwerian lattice into a Boolean lattice
$\def\pw{\mathcal P}$The answer to all the questions is yes. Here are some relevant embedding results:
Proposition 1: Every partial order $(P,\le)$ can be embedded in the powerset lattice $(\pw(P),\su …
- 47.1k