Theorems · Inductive type · general topology
DiscreteTopology
(α : Type u_2) → [t : TopologicalSpace α] → Prop
A topological space is discrete if every set is open, that is,
its topology equals the discrete topology ⊥.
- Defined in
- Mathlib.Topology.Order
- Cited by
- 373 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by413
Results whose statement or proof uses this declaration.
- Module.Basis.ofZLatticeBasisstatement and proof · cited by 36
- isOpen_discretestatement and proof · cited by 36
- IsZLatticestatement · cited by 32
- nhds_discretestatement and proof · cited by 23
- IsEvenlyCoveredproof · cited by 22
- continuous_of_discreteTopologystatement and proof · cited by 20
- Subgroup.strictWidthInftyproof · cited by 19
- Module.Basis.ofZLatticeBasis_applystatement and proof · cited by 11
- isClosed_discretestatement and proof · cited by 9
- stabilizer_isOpenstatement and proof · cited by 9
- isClopen_discretestatement and proof · cited by 8
- discreteTopology_iff_isOpen_singletonstatement and proof · cited by 8
Showing the 200 most cited of 413.