Theorems · Theorem · general topology

ContinuousMap.continuous_compactOpen

∀ {X : Type u_2} {Y : Type u_3} {Z : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → C(Y, Z)},
  Continuous f ↔ ∀ (K : Set Y), IsCompact K → ∀ (U : Set Z), IsOpen U → IsOpen {x | Set.MapsTo (⇑(f x)) K U}

Defined in

Mathlib.Topology.CompactOpen

Cited by

2 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace