Theorems · Inductive type · general topology
IsDiscrete
{X : Type u_5} → [TopologicalSpace X] → Set X → PropA subset s is discrete if the corresponding subtype (with the subspace topology) is a
discrete space.
- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 86 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
Cited by89
Results whose statement or proof uses this declaration.
- IsDiscrete.to_subtypestatement and proof · cited by 8
- DiscreteTopology.isDiscretestatement · cited by 7
- isDiscrete_iff_discreteTopologystatement and proof · cited by 6
- Set.Finite.isDiscretestatement · cited by 6
- IsCompact.finitestatement and proof · cited by 5
- Metric.finite_isBounded_inter_isClosedstatement and proof · cited by 4
- IsDiscrete.nhdsWithinstatement · cited by 4
- IsDiscrete.of_nhdsWithinstatement · cited by 4
- Int.tendsto_coe_cofiniteproof · cited by 4
- nhds_inter_eq_singleton_of_mem_discretestatement and proof · cited by 4
- SetLike.isDiscrete_iff_discreteTopologystatement and proof · cited by 4
- IsClosed.tendsto_coe_cofinite_of_isDiscretestatement and proof · cited by 4