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5 votes
1 answer
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Preimage of a sublocale by a morphism of locales: description by nucleus?

For completeness of MathOverflow, and to avoid any possible misunderstanding, let me recall the following terminology and facts, which should be standard (experts skip the following 2–3 paragraphs ...
Gro-Tsen's user avatar
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2 votes
0 answers
105 views

What is known about sublocales defined by regular nuclei?

(For basic terminology, which is supposed to be standard anyway, see this other question, which inspired this one.) I am interested in nuclei $j\colon L\to L$ on a frame $L$ which are regular elements ...
Gro-Tsen's user avatar
  • 32.5k
3 votes
1 answer
228 views

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 (“...
Gro-Tsen's user avatar
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9 votes
1 answer
372 views

Is an open map with open relative diagonal necessarily a local homeomorphism?

Let $f : X \to Y$ be an open (and continuous) map of locales. Suppose the relative diagonal $\Delta_f : X \to X \times_Y X$ is an open embedding of locales. Does it follow that $f : X \to Y$ is a ...
Zhen Lin's user avatar
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7 votes
2 answers
1k views

Embedding a Brouwerian lattice into a Boolean lattice

I have already asked a similar question at https://math.stackexchange.com/questions/470704/can-a-brouwerian-lattice-be-extended-into-a-boolean-algebra but have received no answer. Sorry, I ask a ...
porton's user avatar
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