Theorems · Theorem · general topology
Filter.EventuallyEq.eq_of_nhds
∀ {X : Type u} [inst : TopologicalSpace X] {α : Type u_1} {x : X} {f g : X → α}, f =ᶠ[nhds x] g → f x = g x- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsstatement and proof · cited by 5,554
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.Eventually.self_of_nhdsproof · cited by 38
Cited by28
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_eq_int_iffproof · cited by 31
- MeromorphicNFAt.meromorphicOrderAt_eq_zero_iffproof · cited by 14
- continuousAt_congrproof · cited by 6
- meromorphicNFAt_toMeromorphicNFAtproof · cited by 5
- toMeromorphicNFAt_eq_selfproof · cited by 4
- AnalyticAt.meromorphicTrailingCoeffAt_of_eq_nhdsNEproof · cited by 4
- HarmonicAt.differentiableAt_complex_partialproof · cited by 3
- SmoothBumpCovering.apply_indproof · cited by 3
- AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iffproof · cited by 3
- meromorphicNFAt_iff_analyticAt_orproof · cited by 3
- circleMap_preimage_codiscreteproof · cited by 3