Theorems · Theorem · general topology

ContinuousMap.hasBasis_nhds

∀ {X : Type u_2} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (f : C(X, Y)),
  (nhds f).HasBasis
    (fun S => S.Finite ∧ ∀ (K : Set X) (U : Set Y), (K, U) ∈ S → IsCompact K ∧ IsOpen U ∧ Set.MapsTo (⇑f) K U) fun x =>
    ⋂ KU ∈ x, {g | Set.MapsTo (⇑g) KU.1 KU.2}

Defined in

Mathlib.Topology.CompactOpen

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace