chore(Topology): Deprecate file

[FormulaRabbit81]

---

• [ ] depends on: #30851 deprecation

[github-actions[bot]]

PR summary 0072a62f20

Import changes exceeding 2%

%	File
+33.70%	Mathlib.Topology.Compactness.HilbertCubeEmbedding

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Compactness.HilbertCubeEmbedding	914	1222	+308 (+33.70%)
Mathlib.Topology.MetricSpace.PiNat	1217	1221	+4 (+0.33%)
M scripts/count-trans-deps.py
M scripts/count-trans-deps.py
M scripts/count-trans-deps.py

Import changes for all files

Files	Import difference
10 files Mathlib.MeasureTheory.Constructions.Polish.Basic Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal Mathlib.MeasureTheory.Constructions.Polish.StronglyMeasurable Mathlib.MeasureTheory.Measure.RegularityCompacts Mathlib.MeasureTheory.Measure.Tight Mathlib.Topology.Algebra.Module.Cardinality Mathlib.Topology.MetricSpace.CantorScheme Mathlib.Topology.MetricSpace.Perfect Mathlib.Topology.MetricSpace.PiNat Mathlib.Topology.MetricSpace.Polish	4
Mathlib.Topology.Compactness.HilbertCubeEmbedding	308

---

Declarations diff

+ continuous_distDenseSeq + continuous_distDenseSeq_inv + distDenseSeq + exists_embedding_to_hilbert_cube + injective_distDenseSeq + separation - exists_closed_embedding_to_hilbert_cube

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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#30851~~ By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.