Theorems · Theorem · general topology
pure_le_nhdsWithin
∀ {α : Type u_1} [inst : TopologicalSpace α] {a : α} {s : Set α}, a ∈ s → pure a ≤ nhdsWithin a s- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 8,121
- nhdsWithinstatement · cited by 1,912
- le_infproof · cited by 107
- Filter.le_principal_iffproof · cited by 87
- pure_le_nhdsproof · cited by 39
Cited by9
Results whose statement or proof uses this declaration.
- mem_of_mem_nhdsWithinproof · cited by 38
- TendstoLocallyUniformlyOn.tendsto_atproof · cited by 11
- IsDiscrete.of_nhdsWithinproof · cited by 4
- tendsto_floor_leftproof · cited by 1
- tendsto_ceil_leftproof · cited by 1
- tendsto_const_nhdsWithinproof · cited by 1
- tendsto_floor_rightproof · cited by 1
- tendsto_ceil_rightproof · cited by 1
- nhdsWithin_of_mem_discreteproof · cited by 0