Theorems · Definition · general topology

BoundedContinuousFunction.toContinuousMapAddMonoidHom

(α : Type u) →
  (R : Type u_2) →
    [inst : TopologicalSpace α] →
      [inst_1 : PseudoMetricSpace R] →
        [inst_2 : AddMonoid R] →
          [inst_3 : BoundedAdd R] → [inst_4 : ContinuousAdd R] → BoundedContinuousFunction α R →+ C(α, R)

The additive map forgetting that a bounded continuous function is bounded.

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Basic

Cited by

3 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePseudoMetricSpaceAddMonoidBoundedAddContinuousAdd