Theorems · Theorem · general topology
pure_le_nhds_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {a b : X}, pure a ≤ nhds b ↔ a = b- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- T1Spacestatement and proof · cited by 275
- specializes_iff_pureproof · cited by 6
- specializes_iff_eqproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- tendsto_rpow_atTop_of_base_lt_oneproof · cited by 2
- one_le_nhds_iffproof · cited by 0
- nonneg_nhds_iffproof · cited by 0