Theorems · Theorem · general topology
LinearOrder.bot_topologicalSpace_eq_preorderTopology
∀ {α : Type u_2} [inst : LinearOrder α] [PredOrder α] [SuccOrder α], ⊥ = Preorder.topology α- Defined in
- Mathlib.Topology.Instances.Discrete
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LinearOrderstatement and proof · cited by 8,572
- Bot.botstatement · cited by 4,720
- OrderTopologyproof · cited by 1,355
- SuccOrderstatement and proof · cited by 574
- PredOrderstatement and proof · cited by 334
- Preorder.topologystatement and proof · cited by 24
- DiscreteTopology.eq_botproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- discreteTopology_iff_orderTopology_of_pred_succproof · cited by 0
- LinearOrder.bot_topologicalSpace_eq_generateFromproof · cited by 0