Theorems · Theorem · general topology
pure_le_nhds
∀ {X : Type u} [inst : TopologicalSpace X], pure ≤ nhds- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- mem_of_mem_nhdsproof · cited by 126
- Filter.mem_pureproof · cited by 14
Cited by39
Results whose statement or proof uses this declaration.
- isCompact_singletonproof · cited by 32
- nhds_discreteproof · cited by 23
- nhdsWithin_singletonproof · cited by 12
- isOpen_singleton_iff_nhds_eq_pureproof · cited by 9
- pure_le_nhdsWithinproof · cited by 9
- HasDerivAt.congr_of_eventuallyEqproof · cited by 8
- tendsto_pure_nhdsproof · cited by 7
- specializes_TFAEproof · cited by 6
- isLindelof_singletonproof · cited by 4
- eq_of_tendsto_nhdsproof · cited by 2
- AffineSpace.nhds_bind_asymptoticNhdsproof · cited by 2
- cauchy_pureproof · cited by 2