Theorems · Theorem · general topology

ContinuousMap.linearIsometryBoundedOfCompact_symm_apply

∀ {α : Type u_1} {E : Type u_3} [inst : TopologicalSpace α] [inst_1 : CompactSpace α]
  [inst_2 : SeminormedAddCommGroup E] {𝕜 : Type u_4} [inst_3 : NormedRing 𝕜] [inst_4 : Module 𝕜 E]
  [inst_5 : IsBoundedSMul 𝕜 E] (f : BoundedContinuousFunction α E),
  (ContinuousMap.linearIsometryBoundedOfCompact α E 𝕜).symm f = f.toContinuousMap

Defined in

Mathlib.Topology.ContinuousMap.Compact

Cited by

0 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCompactSpaceSeminormedAddCommGroupNormedRingModuleIsBoundedSMul