Theorems · Theorem · general topology
isOpen_discrete
∀ {α : Type u_1} [inst : TopologicalSpace α] [DiscreteTopology α] (s : Set α), IsOpen s- Defined in
- Mathlib.Topology.Order
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenstatement · cited by 2,400
- DiscreteTopologystatement and proof · cited by 373
- DiscreteTopology.eq_botproof · cited by 5
Cited by36
Results whose statement or proof uses this declaration.
- nhds_discreteproof · cited by 23
- continuous_of_discreteTopologyproof · cited by 20
- isClosed_discreteproof · cited by 9
- stabilizer_isOpenproof · cited by 9
- discreteTopology_iff_isOpen_singletonproof · cited by 8
- isClopen_discreteproof · cited by 8
- IsLocallyConstant.iff_continuousproof · cited by 4
- IsCoveringMap.isSeparatedMapproof · cited by 4
- IsLocalHomeomorphOn.discreteTopology_of_imageproof · cited by 3
- discreteTopology_iff_forall_isOpenproof · cited by 3
- continuous_discrete_rngproof · cited by 3
- DiscreteTopology.of_continuous_injectiveproof · cited by 2