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feat(Topology/Spectral/ConstructibleTopology): the constructible topology on a compact quasi-separated space X equals the topology generated by the constructible subsets of X#40180

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feat(Topology/Spectral/ConstructibleTopology): the constructible topology on a compact quasi-separated space X equals the topology generated by the constructible subsets of X#40180
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@FMLJohn FMLJohn commented Jun 3, 2026

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In this pull request, I have proved that the constructible topology on a compact quasi-separated space X equals the topology generated by the constructible subsets of X. This holds in particular for spectral spaces.

@FMLJohn FMLJohn added the t-topology Topological spaces, uniform spaces, metric spaces, filters label Jun 3, 2026
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PR summary b9eeed9ae9

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Topology.Spectral.ConstructibleTopology 905 909 +4 (+0.44%)
Import changes for all files
Files Import difference
Mathlib.Topology.Spectral.ConstructibleTopology 4
Mathlib.Topology.Order.GenerateFromLattice (new file) 586

Declarations diff (regex)

+ closure_eq_latticeClosure
+ compl_image_constructibleTopologySubbasis
+ constructibleTopologySubbasis_subset_isConstructible
+ constructibleTopology_eq_generateFrom_isConstructible
+ empty_mem_constructibleTopologySubbasis
+ generateFrom_latticeClosure
+ latticeClosure_constructibleTopologySubbasis

You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

Lean-aware diff — post-build, computed from the Lean environment (commit b9eeed9).

  • +7 new declarations
  • −0 removed declarations
+BooleanSubalgebra.closure_eq_latticeClosure
+compl_image_constructibleTopologySubbasis
+constructibleTopologySubbasis_subset_isConstructible
+constructibleTopology_eq_generateFrom_isConstructible
+empty_mem_constructibleTopologySubbasis
+generateFrom_latticeClosure
+latticeClosure_constructibleTopologySubbasis

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)
Current number Change Type (weak)
5014 1 exposed public sections

Current commit b9eeed9ae9
Reference commit 6ca518ac72

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@FMLJohn FMLJohn changed the title feat(Topology/Spectral/ConstructibleTopology): if X is T0, quasi-compact, quasi-separated and prespectral, then X is T2 in the constructible topology feat(Topology/Spectral/ConstructibleTopology): if a topological space X is T0, quasi-compact, quasi-separated and prespectral, then X is T2 in the constructible topology Jun 3, 2026
@FMLJohn
FMLJohn requested a review from chrisflav June 3, 2026 12:17
Comment thread Mathlib/Topology/Spectral/ConstructibleTopology.lean Outdated
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Note that there is already #39663, which contains this result (and some more) but it was waiting for #39621 to get merged (which was only delegated to me this morning, I'll take care of that ASAP).

@github-actions github-actions Bot added the large-import Automatically added label for PRs with a significant increase in transitive imports label Jun 3, 2026
@FMLJohn FMLJohn changed the title feat(Topology/Spectral/ConstructibleTopology): if a topological space X is T0, quasi-compact, quasi-separated and prespectral, then X is T2 in the constructible topology feat(Topology/Spectral/ConstructibleTopology): the constructible topology on a compact quasi-separated space X equals the topology generated by the constructible subsets of X Jun 3, 2026
@FMLJohn

FMLJohn commented Jun 3, 2026

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Note that there is already #39663, which contains this result (and some more) but it was waiting for #39621 to get merged (which was only delegated to me this morning, I'll take care of that ASAP).

Thank you for letting me know! I have already changed the content of this PR into something else.

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Comment thread Mathlib/Topology/Order.lean Outdated
Comment thread Mathlib/Topology/Order.lean Outdated
Comment thread Mathlib/Topology/Order.lean Outdated
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Comment thread Mathlib/Topology/Spectral/ConstructibleTopology.lean Outdated
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Comment thread Mathlib/Topology/Spectral/ConstructibleTopology.lean Outdated
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@chrisflav chrisflav added the awaiting-author A reviewer has asked the author a question or requested changes. label Jun 5, 2026
@chrisflav chrisflav self-assigned this Jun 5, 2026
FMLJohn and others added 4 commits June 5, 2026 11:50
Co-authored-by: Christian Merten <christian@merten.dev>
Co-authored-by: Christian Merten <christian@merten.dev>
Co-authored-by: Christian Merten <christian@merten.dev>
Co-authored-by: Christian Merten <christian@merten.dev>
@FMLJohn FMLJohn removed the awaiting-author A reviewer has asked the author a question or requested changes. label Jun 5, 2026
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Comment thread Mathlib/Topology/Spectral/ConstructibleTopology.lean
Comment thread Mathlib/Topology/Order.lean Outdated
Comment thread Mathlib/Order/BooleanSubalgebra.lean Outdated
Comment thread Mathlib/Topology/Spectral/ConstructibleTopology.lean Outdated
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Comment thread Mathlib/Topology/Spectral/ConstructibleTopology.lean Outdated
@chrisflav chrisflav added the awaiting-author A reviewer has asked the author a question or requested changes. label Jun 9, 2026
FMLJohn and others added 7 commits June 12, 2026 20:10
Co-authored-by: Christian Merten <christian@merten.dev>
Co-authored-by: Christian Merten <christian@merten.dev>
Co-authored-by: Christian Merten <christian@merten.dev>
Co-authored-by: Christian Merten <christian@merten.dev>
Co-authored-by: Christian Merten <christian@merten.dev>
Co-authored-by: Christian Merten <christian@merten.dev>
@FMLJohn FMLJohn removed the awaiting-author A reviewer has asked the author a question or requested changes. label Jun 12, 2026
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@chrisflav chrisflav added the awaiting-author A reviewer has asked the author a question or requested changes. label Jun 30, 2026
@github-actions github-actions Bot removed the large-import Automatically added label for PRs with a significant increase in transitive imports label Jul 8, 2026
@FMLJohn FMLJohn removed the awaiting-author A reviewer has asked the author a question or requested changes. label Jul 8, 2026
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5 participants