Theorems · Theorem · general topology
DiscreteTopology.isDiscrete
∀ {X : Type u_5} [inst : TopologicalSpace X] {s : Set X} [DiscreteTopology ↑s], IsDiscrete s- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 67 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
- Set.Elemstatement and proof · cited by 7,166
- DiscreteTopologystatement and proof · cited by 373
- IsDiscretestatement · cited by 86
Cited by7
Results whose statement or proof uses this declaration.
- ZLattice.rankproof · cited by 5
- topologicalKrullDim_zero_of_discreteTopologyproof · cited by 2
- AddCircle.isAddQuotientCoveringMap_coeproof · cited by 2
- ZSpan.setFinite_interproof · cited by 1
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1
- ZLattice.FGproof · cited by 1
- ZLattice.summable_norm_sub_rpowproof · cited by 1