Theorems · Theorem · general topology
Set.Finite.isDiscrete
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {s : Set X}, s.Finite → IsDiscrete s- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
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.Finitestatement and proof · cited by 1,814
- T1Spacestatement and proof · cited by 275
- IsDiscretestatement · cited by 86
Cited by6
Results whose statement or proof uses this declaration.
- AddCircle.isAddQuotientCoveringMap_zsmulproof · cited by 2
- codiscrete_le_cofiniteproof · cited by 2
- isQuotientCoveringMap_npowproof · cited by 2
- Liouville.exists_pos_real_of_irrational_rootproof · cited by 1
- Circle.isQuotientCoveringMap_zpowproof · cited by 1
- IsPreconnected.eq_one_or_eq_neg_one_of_sq_eqproof · cited by 1