Theorems · Theorem · functional analysis
Ideal.Quotient.norm_mk_lt
∀ {R : Type u_3} [inst : SeminormedCommRing R] {I : Ideal R} (x : R ⧸ I) {ε : ℝ},
0 < ε → ∃ r, (Ideal.Quotient.mk I) r = x ∧ ‖r‖ < ‖x‖ + ε- Defined in
- Mathlib.Analysis.Normed.Group.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommRing
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- Norm.normstatement · cited by 5,413
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.Quotient.mkstatement · cited by 610
- SeminormedCommRingstatement and proof · cited by 38
- QuotientAddGroup.exists_norm_mk_ltproof · cited by 3
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