Theorems · Theorem · functional analysis

BoundedContinuousFunction.norm_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

3 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceNonUnitalSeminormedRingIsCancelMulZero