Mathlib Map

Theorems · Theorem · general topology

ContinuousAt.lowerHemicontinuousAt

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {x : α},
  ContinuousAt f x → LowerHemicontinuousAt (fun x => {f x}) x

Alias of the reverse direction of lowerHemicontinuousAt_singleton_iff.

Defined in
Mathlib.Topology.Semicontinuity.Hemicontinuity
Cited by
0 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceContinuousAt · cited by 697ContinuousAtLowerHemicontinuousAt · cited by 15LowerHemicontinuousAtlowerHemicontinuousAt_singleton_iff · cited by 1lowerHemicontinuousAt_sin…ContinuousAt.lowerHemicontinu…CITED BYCITES

Cites5

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.