Theorems · Theorem · general topology
lim_nhdsWithin
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {x : X} {s : Set X}, x ∈ closure s → (nhdsWithin x s).lim = x- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- nhdsWithinstatement · cited by 1,912
- T2Spacestatement and proof · cited by 1,351
- closurestatement and proof · cited by 1,254
- inf_le_leftproof · cited by 286
- Filter.limstatement · cited by 10
- lim_eqproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- limUnder_nhdsWithin_idproof · cited by 0