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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.
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 …
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 …