Theorems · Theorem · general topology
ContinuousMap.norm_sub_eq_max
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : CompactSpace α] {R : Type u_4}
[inst_2 : NonUnitalSeminormedRing R] [IsCancelMulZero R] {f g : C(α, R)}, f * g = 0 → ‖f - g‖ = max ‖f‖ ‖g‖- Defined in
- Mathlib.Topology.ContinuousMap.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement and proof · cited by 5,413
- ContinuousMapstatement and proof · cited by 2,491
- sub_eq_add_negproof · cited by 1,023
- CompactSpacestatement and proof · cited by 593
- mul_negproof · cited by 590
- norm_negproof · cited by 190
- IsCancelMulZerostatement and proof · cited by 177
- NonUnitalSeminormedRingstatement and proof · cited by 44
- ContinuousMap.norm_add_eq_maxproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.nnnorm_sub_eq_maxproof · cited by 0