Theorems · Theorem · general topology
isDiscrete_iff_discreteTopology
∀ {X : Type u_5} [inst : TopologicalSpace X] {s : Set X}, IsDiscrete s ↔ DiscreteTopology ↑s- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.Elemstatement and proof · cited by 7,166
- DiscreteTopologystatement and proof · cited by 373
- IsDiscretestatement and proof · cited by 86
- IsDiscrete.to_subtypeproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- ae_restrict_le_codiscreteWithinproof · cited by 4
- isDiscrete_iff_forall_mem_exists_isOpenproof · cited by 3
- isDiscrete_iff_nhdsNEproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top_iffproof · cited by 1
- discreteTopology_unionproof · cited by 0
- IsPreconnected.isDiscrete_iff_subsingletonproof · cited by 0