Theorems · Definition · general topology
specializationOrder
(X : Type u_3) → [inst : TopologicalSpace X] → [T0Space X] → PartialOrder X
Specialization forms a partial order on a t0 topological space.
- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpaceT0Space
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.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderproof · cited by 7,952
- PartialOrderstatement and proof · cited by 6,410
- nhdsproof · cited by 5,554
- OrderDual.toDualproof · cited by 481
- T0Spacestatement and proof · cited by 179
- nhds_injectiveproof · cited by 2
- specializationPreorderproof · cited by 2
- PartialOrder.le_antisymmproof · cited by 1
- PartialOrder.liftproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- irreducibleSetEquivPointsstatement · cited by 3
- Topology.IsOpenEmbedding.coheight_eqstatement · cited by 1
- irreducibleSetEquivPoints.congr_simpstatement · cited by 0
- coe_irreducibleEquivPoints_symm_applystatement · cited by 0