Theorems · Definition · general topology

ContinuousMap.evalCLM

{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] → α → C(α, M) →L[R] M

Evaluation at a point, as a continuous linear map.

Defined in

Mathlib.Topology.ContinuousMap.Algebra

Cited by

4 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceSemiringAddCommMonoidContinuousAddModuleContinuousConstSMul