Theorems · Theorem · general topology
DiscreteTopology.eq_bot
∀ {α : Type u_2} {t : TopologicalSpace α} [self : DiscreteTopology α], t = ⊥The TopologicalSpace structure on a type with discrete topology is equal to ⊥.
- Defined in
- Mathlib.Topology.Order
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DiscreteTopology
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Bot.botstatement · cited by 4,720
- DiscreteTopologystatement and proof · cited by 373
Cited by5
Results whose statement or proof uses this declaration.
- isOpen_discreteproof · cited by 36
- LinearOrder.bot_topologicalSpace_eq_preorderTopologyproof · cited by 2
- isClosedEmbedding_of_spaced_outproof · cited by 1
- InfiniteGalois.algEquivToLimit_continuousproof · cited by 0
- discreteTopology_iff_orderTopology_of_pred_succproof · cited by 0