Theorems · Definition · general topology
specializationPreorder
(X : Type u_1) → [TopologicalSpace X] → Preorder X
Specialization forms a preorder on the topological space.
- Defined in
- Mathlib.Topology.Defs.Filter
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Preorderstatement and proof · cited by 7,952
- nhdsproof · cited by 5,554
- OrderDual.toDualproof · cited by 481
- Preorder.lt_iff_le_not_geproof · cited by 1
- Preorder.le_transproof · cited by 1
- Preorder.le_reflproof · cited by 1
- Preorder.liftproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- specializationOrderproof · cited by 3
- Continuous.specialization_monotonestatement · cited by 3
- closure_singleton_eq_Iicstatement · cited by 3