Theorems · Theorem · general topology

ContinuousMap.coeFnLinearMap_apply

∀ {α : Type u_1} [inst : TopologicalSpace α] (R : Type u_3) {M : Type u_5} [inst_1 : TopologicalSpace M]
  [inst_2 : Semiring R] [inst_3 : AddCommMonoid M] [inst_4 : ContinuousAdd M] [inst_5 : Module R M]
  [inst_6 : ContinuousConstSMul R M] (a : C(α, M)) (a_1 : α),
  (ContinuousMap.coeFnLinearMap R) a a_1 = (↑ContinuousMap.coeFnAddMonoidHom).toFun a a_1

Defined in

Mathlib.Topology.ContinuousMap.Algebra

Cited by

0 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceSemiringAddCommMonoidContinuousAddModuleContinuousConstSMul