Theorems · Theorem · general topology

ContinuousAddMonoidHom.locallyCompactSpace_of_equicontinuousAt

∀ {X : Type u_7} {Y : Type u_8} [inst : TopologicalSpace X] [inst_1 : AddGroup X] [IsTopologicalAddGroup X]
  [inst_3 : UniformSpace Y] [inst_4 : AddCommGroup Y] [IsUniformAddGroup Y] [T0Space Y] [CompactSpace Y] (U : Set X)
  (V : Set Y), IsCompact U → V ∈ nhds 0 → EquicontinuousAt (fun f => ⇑↑f) 0 → LocallyCompactSpace (X →ₜ+ Y)

Defined in

Mathlib.Topology.Algebra.Group.CompactOpen

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddGroupIsTopologicalAddGroupUniformSpaceAddCommGroupIsUniformAddGroupT0SpaceCompactSpace