Theorems · Theorem · functional analysis

BoundedContinuousFunction.nnnorm_add_eq_max

∀ {α : Type u} [inst : TopologicalSpace α] {R : Type u_1} [inst_1 : NonUnitalSeminormedRing R] [IsCancelMulZero R]
  {f g : BoundedContinuousFunction α R}, f * g = 0 → ‖f + g‖₊ = max ‖f‖₊ ‖g‖₊

If the product of bounded continuous functions is zero, then the norm of their sum is the maximum of their norms.

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Normed

Cited by

1 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceNonUnitalSeminormedRingIsCancelMulZero