Theorems · Definition · general topology

LocallyConstant.toContinuousMapLinearMap

{X : Type u_1} →
  {Y : Type u_2} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] →
        (R : Type u_3) →
          [inst_2 : Semiring R] →
            [inst_3 : AddCommMonoid Y] →
              [inst_4 : Module R Y] →
                [inst_5 : ContinuousAdd Y] → [inst_6 : ContinuousConstSMul R Y] → LocallyConstant X Y →ₗ[R] C(X, Y)

The inclusion of locally-constant functions into continuous functions as a linear map.

Defined in

Mathlib.Topology.ContinuousMap.LocallyConstant

Cited by

3 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceSemiringAddCommMonoidModuleContinuousAddContinuousConstSMul