Theorems · Theorem · general topology
specializes_iff_pure
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X}, x ⤳ y ↔ pure x ≤ nhds y- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- IsOpenproof · cited by 2,400
- IsClosedproof · cited by 1,639
- closureproof · cited by 1,254
- List.TFAE.outproof · cited by 177
- Specializesstatement and proof · cited by 176
- ClusterPtproof · cited by 138
- specializes_TFAEproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- pure_le_nhds_iffproof · cited by 3
- Specializes.map_of_continuousWithinAtproof · cited by 3
- Filter.HasBasis.specializes_iffproof · cited by 2
- specializes_of_nhdsWithinproof · cited by 1
- LinearMap.antilipschitz_of_comap_nhds_leproof · cited by 1
- Specializes.pure_le_nhdsproof · cited by 0