Theorems · Theorem · general topology
eventuallyEq_nhdsWithin_of_eqOn
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {f g : α → β} {s : Set α} {a : α},
Set.EqOn f g s → f =ᶠ[nhdsWithin a s] g- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- nhdsWithinstatement · cited by 1,912
- Filter.EventuallyEqstatement · cited by 1,912
- Set.EqOnstatement and proof · cited by 603
- Filter.mem_inf_of_rightproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- tendsto_nhdsWithin_congrproof · cited by 6
- Set.EqOn.eventuallyEq_nhdsWithinproof · cited by 5
- meromorphicTrailingCoeffAt_invproof · cited by 1
- Function.Periodic.cuspFunction_zero_eq_limUnder_nhds_neproof · cited by 1