Theorems · Theorem · general topology

ContinuousMap.nnnorm_add_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‖₊

If the product of continuous functions on a compact space is zero, then the norm of their sum is the maximum of their norms.

Defined in

Mathlib.Topology.ContinuousMap.Compact

Cited by

1 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCompactSpaceNonUnitalSeminormedRingIsCancelMulZero