Theorems · Theorem · general topology
eventually_ne_nhds
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {a b : X}, a ≠ b → ∀ᶠ (x : X) in nhds a, x ≠ b- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpaceT1Space
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.
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsstatement · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- T1Spacestatement and proof · cited by 275
- IsOpen.eventually_memproof · cited by 24
- isOpen_neproof · cited by 22
Cited by7
Results whose statement or proof uses this declaration.
- HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_divproof · cited by 3
- eventually_ne_nhdsWithinproof · cited by 3
- Real.deriv2_mul_logproof · cited by 2
- Real.deriv2_qaryEntropyproof · cited by 2
- MeromorphicAt.eventually_analyticAtproof · cited by 1
- MeromorphicAt.eventually_continuousAtproof · cited by 1
- MeasureTheory.integral_Ioi_deriv_mul_eq_subproof · cited by 1