Theorems · Theorem · functional analysis

LinearMap.toContPerfPair_apply

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : TopologicalSpace R]
  [inst_2 : AddCommGroup M] [inst_3 : Module R M] [inst_4 : TopologicalSpace M] [inst_5 : AddCommGroup N]
  [inst_6 : Module R N] [inst_7 : TopologicalSpace N] (p : M →ₗ[R] N →ₗ[R] R) [inst_8 : p.IsContPerfPair]
  [inst_9 : IsTopologicalRing R] (x : M) (y : N), (p.toContPerfPair x) y = (p x) y

Defined in

Mathlib.Topology.Algebra.Module.PerfectPairing

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingTopologicalSpaceAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceLinearMap.IsContPerfPairIsTopologicalRing