Theorems · Theorem · general topology
ContinuousMap.nnnorm_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
- 0 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- NNRealstatement · cited by 4,310
- ContinuousMapstatement and proof · cited by 2,491
- NNNorm.nnnormstatement · cited by 952
- CompactSpacestatement and proof · cited by 593
- NNReal.eqproof · cited by 201
- IsCancelMulZerostatement and proof · cited by 177
- NonUnitalSeminormedRingstatement and proof · cited by 44
- ContinuousMap.norm_sub_eq_maxproof · cited by 1
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