feat: better API for T1Space and DiscreteSpace on quotients by non-normal subgroups
#30383
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…n-normal subgroups
ADedecker
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awaiting-CI
t-topology
PR summary c4b0fc93a3
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.Topology.Algebra.Group.ClosedSubgroup | 1123 | 1125 | +2 (+0.18%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.Topology.Algebra.ClosedSubgroup Mathlib.Topology.Algebra.Group.ClosedSubgroup |
2 |
Declarations diff
+ discreteTopology
+ instT1Space
+ preimage_mk_one
++ discreteTopology_iff
++ t1Space_iff
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>The doc-module for script/declarations_diff.sh contains some details about this script.
No changes to technical debt.
You can run this locally as
./scripts/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
ADedecker
commented
Oct 10, 2025
Comment on lines
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| /-- The quotient of a topological group `G` by a closed subgroup `N` is T1. | ||
| When `G` is normal, this implies (because `G ⧸ N` is a topological group) that the quotient is T3 | ||
| (see `QuotientGroup.instT3Space`). | ||
| Back to the general case, we will show later that the quotient is in fact T2 | ||
| since `N` acts on `G` properly. -/ |
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The T2 instance is added in #30387
The reason I think those instances should coexist is this one only requires ContinuousMul (or even separate continuity of the multiplication in fact)
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This pull request has conflicts, please merge |
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This is motivated by #29743, which led me to realize that the current proof of Subgroup.isOpen_of_isClosed_of_finiteIndex is quite complicated. Morally, the proof should be "
G / His T1 becauseHis closed, finite becauseHhas finite index inG, hence it is discrete, henceHis open".The issue is that too much of our API on quotient groups (and in particular the separation criterion) was restricted to quotients by normal subgroups. This PR fixes this, and cleans some things along the way.