Theorems · Theorem · functional analysis
AddSubgroup.norm_normedMk
∀ {M : Type u_1} [inst : SeminormedAddCommGroup M] (S : AddSubgroup M),
↑S.topologicalClosure ≠ Set.univ → ‖S.normedMk‖ = 1The operator norm of the projection is 1 if the subspace is not dense.
- Defined in
- Mathlib.Analysis.Normed.Group.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- SetLike.coestatement and proof · cited by 8,199
- Norm.normstatement and proof · cited by 5,413
- Set.univstatement and proof · cited by 3,945
- AddSubgroupstatement and proof · cited by 3,232
- Compl.complproof · cited by 2,925
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HasQuotient.Quotientstatement · cited by 2,301
- le_antisymmproof · cited by 2,068
- norm_nonnegproof · cited by 725
- QuotientAddGroup.mkproof · cited by 348
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