ContinuousMap.homeoFnOfDiscrete

{X : Type u_2} →
  {Y : Type u_3} →
    [inst : TopologicalSpace X] → [inst_1 : TopologicalSpace Y] → [DiscreteTopology X] → C(X, Y) ≃ₜ (X → Y)

The continuous functions from X to Y are the same as the plain functions when X is discrete.

Defined in: Mathlib.Topology.CompactOpen
Cited by: 6 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace DiscreteTopology

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.