Theorems · Theorem · general topology
ContinuousAt.restrict
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set X}
{t : Set Y} (h1 : Set.MapsTo f s t) {x : ↑s}, ContinuousAt f ↑x → ContinuousAt (Set.MapsTo.restrict f s t h1) x- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- Set.MapsTostatement and proof · cited by 732
- ContinuousAtstatement and proof · cited by 697
- Set.MapsTo.restrictstatement · cited by 57
- ContinuousAt.compproof · cited by 56
- continuousAt_subtype_valproof · cited by 9
- ContinuousAt.codRestrictproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousAt.restrictPreimageproof · cited by 0