feat(Topology/Group): Lemmas about profinite group

[Thmoas-Guan]

A lemma stating a topological group that has a ContinuousMulEquiv to a profinite group is profinite.
With addition of a lemma Homeomorph.totallyDisconnectedSpace

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[github-actions]

PR summary 325676a2f1

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ ContinuousAddEquiv
+ ContinuousMulEquiv
+ apply_eq_iff_eq
+ apply_eq_iff_symm_apply
+ apply_symm_apply
+ bijective
+ coe_mk
+ coe_mk'
+ coe_refl
+ coe_toHomeomorph_symm
+ coe_trans
+ comp_symm_eq
+ eq_comp_symm
+ eq_symm_apply
+ eq_symm_comp
+ equivLike_inv_eq_symm
+ ext
+ injective
+ instance : CoeFun (M ≃ₜ* N) fun _ ↦ M → N
+ instance : EquivLike (M ≃ₜ* N) M N
+ instance : HomeomorphClass (M ≃ₜ* N) M N
+ instance : Inhabited (M ≃ₜ* M) := ⟨ContinuousMulEquiv.refl M⟩
+ instance : MulEquivClass (M ≃ₜ* N) M N
+ instance {M N} [Unique M] [Unique N] [Mul M] [Mul N]
+ invFun_eq_symm
+ mk'
+ ofContinuousMulEquiv
+ ofUnique
+ refl
+ refl_apply
+ self_comp_symm
+ self_trans_symm
+ surjective
+ symm
+ symm_apply_apply
+ symm_apply_eq
+ symm_comp_eq
+ symm_comp_self
+ symm_symm
+ symm_trans_apply
+ symm_trans_self
+ toEquiv_eq_coe
+ toHomeomorph_eq_coe
+ toMulEquiv_eq_coe
+ totallyDisconnectedSpace
+ trans
+ trans_apply

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.

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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).