Theorems · Theorem · general topology
continuousWithinAt_compl_self
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {x : α},
ContinuousWithinAt f {x}ᶜ x ↔ ContinuousAt f x- Defined in
- Mathlib.Topology.ContinuousOn
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Compl.complstatement · cited by 2,925
- ContinuousAtstatement and proof · cited by 697
- ContinuousWithinAtstatement and proof · cited by 512
- Set.compl_eq_univ_sdiffproof · cited by 43
- continuousWithinAt_univproof · cited by 22
- continuousWithinAt_sdiff_selfproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Complex.differentiableOn_update_limUnder_of_isLittleOproof · cited by 4
- continuousAt_of_not_accPtproof · cited by 1
- DirichletCharacter.differentiable_LFunctionTrivChar₁proof · cited by 1