Theorems · Theorem · general topology
Ne.nhdsWithin_compl_singleton
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {x y : X}, x ≠ y → nhdsWithin x {y}ᶜ = nhds x- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 4 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- T1Spacestatement and proof · cited by 275
- isOpen_neproof · cited by 22
- IsOpen.nhdsWithin_eqproof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- hasFDerivWithinAt_congr_set'proof · cited by 5
- isOpen_setOfPred_eventually_nhdsWithinproof · cited by 2
- nhdsWithin_compl_singleton_leproof · cited by 2
- preperfect_iff_perfect_closureproof · cited by 0