Smallest filter #915
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Smallest filter #915
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zstone1
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CohenCyril
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May 2, 2023
theories/topology.v
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| @@ -2133,6 +2180,25 @@ move=> ?; apply: (card_le_trans (card_image_le _ _)). | |||
| exact: fset_subset_countable. | |||
| Qed. | |||
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| Lemma smallest_filter_finI {T : choiceType} (D : set T) f : | |||
| D!=set0 -> filter_from (finI_from D f) id = smallest (@Filter T) (f @` D). | |||
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Suggested change
| D!=set0 -> filter_from (finI_from D f) id = smallest (@Filter T) (f @` D). | |
| D !=set0 -> filter_from (finI_from D f) id = smallest (@Filter T) (f @` D). |
Also.
Could this be decomposed into:
filter_from D f = smallest superset_closed (f @D)`finI_from D f = smallest finI_closed (f @D)`smallest Filter X = setT|smallest superset_closed (smallest finI_closed X)
? (and maybe other variations withsetTor with nonemptyness ofX)
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Probably yes. I just proved the relationship I needed for my Urysohn's Lemma stuff. But these other variants are likely helpful elsewhere (E.G. with the sup topology). I'd rather add them in a separate PR, though.
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Thanks for the review. Turns out putting a |
CohenCyril
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Jun 27, 2023
CohenCyril
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Jun 27, 2023
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* various forms of smallest filters Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
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* various forms of smallest filters Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
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* various forms of smallest filters Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
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TODO: MC2 port
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* various forms of smallest filters Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
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Motivation for this change
Splitting up the boring part of #900, this just shows that the following are all equivalent
Smallest filter Ffilter_from (\bigcup_n (smallest_filter_stage F n))(E.G. set of all pairwise intersections)filter_from (finI_from F)It also adds a notion of
set_nbhs A, which is the filter from all open sets containingA.I also added a gitignore for the
toolsrepo. Is this correct? If not, how else am I supposed to use the changelog generator?Things done/to do
CHANGELOG_UNRELEASED.mdCompatibility with MathComp 2.0
TODO: HB portto make sure someone ports this PR tothe
hierarchy-builderbranch or I already opened an issue or PR (please cross reference).Automatic note to reviewers
Read this Checklist and put a milestone if possible.