feat(Topology): subspace of a perfectly normal space is perfectly normal

[CoolRmal]

The mains theorems proved in this PR are

• A topological space is perfectly normal iff every closed set is the zero set of a continuous
  function taking values in the unit interval.
• Every subspace of a perfectly normal space is perfectly normal.

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[github-actions]

PR summary 5fc0241932

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.Separation.PerfectlyNormal (new file)	1540

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Declarations diff

+ IsClosed.image_val
+ IsOpen.image_val
+ SeparatedNhds.of_finite
+ Topology.IsEmbedding.perfectlyNormalSpace
+ image_eq_isClosed_inter_range
+ image_eq_isOpen_inter_range
+ instance {s : Set X} [PerfectlyNormalSpace X] : PerfectlyNormalSpace s
+ perfectlyNormalSpace_iff_forall_isClosed_preimage_zero

You can run this locally as follows

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

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

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

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).

[CoolRmal]

!bench

[leanprover-radar]

Benchmark results for e8e7e40 against 5fc0241 are in. There are significant results. @CoolRmal

• 🟥 main exited with code 1

No significant changes detected.