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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 9 months |
| seen | Apr 5 at 20:37 | |
| stats | profile views | 2 |
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Apr 2 |
accepted | does this property of a lattice have a commonly used name? |
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Apr 2 |
comment |
does this property of a lattice have a commonly used name? of course, I was being silly. thanks. |
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Apr 2 |
asked | does this property of a lattice have a commonly used name? |
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Aug 9 |
comment |
topology on the set of partitions Building on the answer from @JDH, another approach is to endow the set with the interval topology, defined for example here. Then, there is a result (e.g., Birkhoff 1995) that says: A lattice in its interval topology is compact if and only if it is complete. $X$, $Y$ and the set of all partitions are all complete and thus compact. |
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Aug 9 |
awarded | Scholar |
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Aug 9 |
accepted | topology on the set of partitions |
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Aug 9 |
comment |
topology on the set of partitions @AsafKaragila: The comments about Vitali sets was simply meant to illustrate one of the ways that the set of all partitions differs from the set of partitions whose elements are measurable; there was no claim that the Vitali sets are the only difference. Re: J.Loreaux's comment: Both $X$ and $Y$ are sets of all (thus arbitrary) partitions satisfying a given condition on the elements. |
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Aug 9 |
revised |
topology on the set of partitions provided additional context for the question |
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Aug 9 |
awarded | Supporter |
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Aug 9 |
comment |
topology on the set of partitions @JDH - Thanks, that's a very clear and helpful answer. Any thoughts on whether the set of all partitions (or sets X and Y above) is compact in the lower-cone topology? |
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Aug 8 |
awarded | Editor |
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Aug 8 |
revised |
topology on the set of partitions added an (imprecise) conjecture about a related set |
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Aug 8 |
awarded | Student |
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Aug 8 |
asked | topology on the set of partitions |
