Theorems · Theorem · general topology
specializes_iff_inseparable
∀ {X : Type u_1} [inst : TopologicalSpace X] [R0Space X] {x y : X}, x ⤳ y ↔ Inseparable x yIn an R₀ space, Specializes is equivalent to Inseparable.
- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpaceR0Space
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Specializesstatement and proof · cited by 176
- Inseparablestatement · cited by 160
- R0Spacestatement and proof · cited by 22
- Inseparable.specializesproof · cited by 16
- Specializes.antisymmproof · cited by 9
- Specializes.symmproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Filter.HasBasis.inseparable_iff_uniformityproof · cited by 5
- disjoint_nhds_nhds_iff_not_inseparableproof · cited by 2
- addGroup_inseparable_iffproof · cited by 1
- Specializes.inseparableproof · cited by 1
- group_inseparable_iffproof · cited by 0