Theorems · Theorem · general topology
continuousOn_singleton
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] (f : α → β) (a : α),
ContinuousOn f {a}- Defined in
- Mathlib.Topology.ContinuousOn
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- ContinuousOnstatement · cited by 1,411
- mem_of_mem_nhdsproof · cited by 126
- nhdsWithin_singletonproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- cfc_algebraMapproof · cited by 8
- DiffContOnCl.continuousOn_ballproof · cited by 6
- InnerProductSpace.HarmonicContOnCl.continuousOn_ballproof · cited by 1
- Set.Subsingleton.continuousOnproof · cited by 0