feat(Topology/Separation/NotNormal): generalize to non-separable spaces

[peakpoint]

---

[github-actions]

PR summary cfceff4198

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Separation.NotNormal	1421	660	-761 (-53.55%)

Import changes for all files

Files	Import difference
Mathlib.Topology.Separation.NotNormal	-761

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Declarations diff

+ mk_lt_continuum
+ mk_lt_two_pow_mk_dense
+ not_normal_of_continuum_le_mk
+ not_normal_of_mk_two_pow_dense_le_mk_two_pow
+ not_normal_of_two_pow_mk_dense_le_mk
+ two_pow_mk_le_two_pow_mk_dense
+ two_pow_mk_lt_continuum
- IsClosed.mk_lt_continuum
- IsClosed.not_normal_of_continuum_le_mk

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 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).

[ocfnash]

Thanks!

One optional suggestion to trim some lemmas.

bors d+

[ocfnash]

Unless you need these for an application, I wouldn't bother adding these:

Suggested change

	theorem not_normal_of_mk_two_pow_dense_le_mk_two_pow {s d : Set X} (hs : IsClosed s)
	[DiscreteTopology s] (hd : Dense d) (hds : (2 : Cardinal) ^ #d < 2 ^ #s) : ¬NormalSpace X :=
	fun _ ↦ (hs.two_pow_mk_le_two_pow_mk_dense hd).not_gt hds
	theorem not_normal_of_two_pow_mk_dense_le_mk {s d : Set X} (hs : IsClosed s)
	[DiscreteTopology s] (hd : Dense d) (hds : 2 ^ #d ≤ #s) : ¬NormalSpace X :=
	fun _ ↦ (hs.mk_lt_two_pow_mk_dense hd).not_ge hds

(I'm even a bit dubious about mk_lt_two_pow_mk_dense, though I do think it's worth having.)

[mathlib-bors]

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