Theorems · Theorem · general topology

ContinuousMap.nhds_compactOpen

∀ {X : Type u_2} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (f : C(X, Y)),
  nhds f =
    ⨅ K,
      ⨅ (_ : IsCompact K),
        ⨅ U, ⨅ (_ : IsOpen U), ⨅ (_ : Set.MapsTo (⇑f) K U), Filter.principal {g | Set.MapsTo (⇑g) K U}

Defined in

Mathlib.Topology.CompactOpen

Cited by

4 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace