Theorems · Theorem · general topology
nhdsWithin_compl_singleton_le
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] (x y : X), nhdsWithin x {x}ᶜ ≤ nhdsWithin x {y}ᶜ- 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.
Cites10
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 and proof · cited by 8,121
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- eq_or_neproof · cited by 1,117
- Eq.leproof · cited by 605
- T1Spacestatement and proof · cited by 275
- nhdsWithin_le_nhdsproof · cited by 145
- Ne.nhdsWithin_compl_singletonproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- preimage_extChartAt_eventuallyEq_compl_singletonproof · cited by 3
- eventuallyEq_insertproof · cited by 2