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[Merged by Bors] - feat(Mathlib/Topology/Bases): subbasis closed under intersection is a basis #12221

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@mans0954 mans0954 commented Apr 17, 2024

We show that if a sub-basis is closed under finite intersections, then it is a basis for a topology.

As a corollary, if a sub-basis is closed under intersections, then inserting the universal set gives a basis for the topology.

An example application of this result is given in #12234


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@mans0954 mans0954 added awaiting-review t-topology Topological spaces, uniform spaces, metric spaces, filters labels Apr 17, 2024
@mans0954 mans0954 requested a review from ADedecker April 30, 2024 10:38
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github-actions bot commented Jun 7, 2024

Import summary

Dependency changes
File Base Count Head Count Change
Mathlib.Topology.Bases 587 588 +1 (+0.17%)

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github-actions bot commented Jun 15, 2024

PR summary d07418dc3d

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Topology.Bases 604 605 +1 (+0.17%)
Import changes for all files
Files Import difference
Too many changes (1342)!

Declarations diff

+ generateFrom_insert_of_generateOpen
+ generateFrom_insert_univ
+ isTopologicalBasis_of_subbasis_of_finiteInter
+ isTopologicalBasis_of_subbasis_of_inter
+ mk₂

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

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back for more in a bit.

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Here are some simplifications for you.

@j-loreaux j-loreaux self-assigned this Jul 14, 2024
@j-loreaux j-loreaux added the awaiting-author A reviewer has asked the author a question or requested changes label Jul 14, 2024
mans0954 and others added 4 commits July 14, 2024 06:42
…nprover-community/mathlib4 into mans0954/subbasis-closed-under-inter
@mans0954 mans0954 removed the awaiting-author A reviewer has asked the author a question or requested changes label Jul 14, 2024
@j-loreaux j-loreaux changed the title feat(Mathlib/Topology/Bases): Subbasis closed under intersection feat(Mathlib/Topology/Bases): subbasis closed under intersection is a basis Jul 15, 2024
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bors merge

@github-actions github-actions bot added the ready-to-merge This PR has been sent to bors. label Jul 15, 2024
mathlib-bors bot pushed a commit that referenced this pull request Jul 15, 2024
… basis (#12221)

We show that if a sub-basis is closed under finite intersections, then it is a basis for a topology.

As a corollary, if a sub-basis is closed under intersections, then inserting the universal set gives a basis for the topology.

An example application of this result is given in #12234



Co-authored-by: Christopher Hoskin <[email protected]>
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mathlib-bors bot commented Jul 15, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(Mathlib/Topology/Bases): subbasis closed under intersection is a basis [Merged by Bors] - feat(Mathlib/Topology/Bases): subbasis closed under intersection is a basis Jul 15, 2024
@mathlib-bors mathlib-bors bot closed this Jul 15, 2024
@mathlib-bors mathlib-bors bot deleted the mans0954/subbasis-closed-under-inter branch July 15, 2024 17:07
@adomani adomani mentioned this pull request Aug 1, 2024
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3 participants