Theorems · Theorem · general topology
Ne.nhdsWithin_sdiff_singleton
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {x y : X},
x ≠ y → ∀ (s : Set X), nhdsWithin x (s \ {y}) = nhdsWithin x s- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Filterstatement and proof · cited by 8,121
- Compl.complproof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- IsOpen.mem_nhdsproof · cited by 470
- Set.inter_commproof · cited by 291
- T1Spacestatement and proof · cited by 275
- Set.sdiff_eqproof · cited by 59
- mem_nhdsWithin_of_mem_nhdsproof · cited by 50
- isOpen_neproof · cited by 22
- nhdsWithin_inter_of_memproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- Complex.differentiableOn_compl_singleton_and_continuousAt_iffproof · cited by 4
- Ne.nhdsWithin_diff_singletonproof · cited by 0