Theorems · Theorem · functional analysis
SeparationQuotient.norm_normedMk_eq_one
∀ {M : Type u_1} [inst : SeminormedAddCommGroup M] [NontrivialTopology M], ‖SeparationQuotient.normedMk‖ = 1The operator norm of the projection is 1 if there is an element whose norm is different from
0.
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- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_rflproof · cited by 1,558
- norm_nonnegproof · cited by 725
- zero_le_oneproof · cited by 316
- NormedAddGroupHomstatement · cited by 216
- lt_of_le_of_ne'proof · cited by 149
- SeparationQuotientstatement · cited by 128
- NontrivialTopologystatement and proof · cited by 46
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