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7 questions
4
votes
1
answer
195
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Consistency of the Hurewicz dichotomy property
Just to fix the environment, let's work in the Baire space $\omega^\omega$, the space of infinite sequences of natural numbers with the product of the discrete topology over $\omega$. We say that a ...
- 2,286
7
votes
1
answer
181
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Lachlan on topology for priority arguments
There is a set of notes by Lachlan from 1973 on casting priority arguments in topological language; references to these notes are few and far between, but one source refers to them as "Topology for ...
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0
votes
0
answers
173
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Minimum regular open set containing a given set in a T0 Alexandrov topological space
What is known about the minimum regular open set containing a given set in a T$_0$ Alexandrov topological space? I'm particularly interested in the condition for the minimum set happening to be first-...
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8
votes
2
answers
537
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A continuous notion of realizability
I have been interested in non-classical logics, off and on, for quite a while. This question is probably very basic, and I hope it is not too low-level for MO. My question stems from an attempt to ...
- 20.9k
2
votes
0
answers
369
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Constructing the Stone space of a distributive lattice
Does anyone have a good reference for the method of giving a topology to a distributive lattice as outlined in M.H. Stone's "Topological representation of distributive lattices and Brouwerian ...
- 10.4k
23
votes
3
answers
2k
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An ultrafilter is a set of subsets containing exactly one element of each finite partition: reference request
There are probably dozens of ways of defining "ultrafilter". The definition I've seen most often involves first defining "filter", then declaring an ultrafilter to be a maximal filter.
But there's ...
- 27.7k
6
votes
1
answer
678
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Is it possible to define a closure operator in terms of partial ordering?
For boolean algebra, let's take Roman Sikorski's Boolean Algebras as our reference. After giving a set of axioms, he proves (p.9) that the join of A and B is the least element of the algebra such that ...
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