Theorems · Definition · functional analysis
QuotientGroup.quotientQuotientIsometryEquivQuotient
{M : Type u_1} →
[inst : SeminormedCommGroup M] → {S T : Subgroup M} → S ≤ T → (M ⧸ S) ⧸ Subgroup.map (QuotientGroup.mk' S) T ≃ᵢ M ⧸ TAn isometric version of QuotientGroup.quotientQuotientEquivQuotient.
- Defined in
- Mathlib.Analysis.Normed.Group.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
Around this declaration
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- MulEquivproof · cited by 1,142
- Subgroup.mapstatement and proof · cited by 301
- SeminormedCommGroupstatement and proof · cited by 191
- IsometryEquivstatement · cited by 177
- MulEquiv.toEquivproof · cited by 126
- QuotientGroup.mk'statement and proof · cited by 90
- QuotientGroup.quotientQuotientEquivQuotientproof · cited by 1
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