Theorems · Theorem · general topology
IsCompact.codiscreteWithin_eq
∀ {X : Type u_1} [inst : TopologicalSpace X] {K : Set X} [T1Space X],
IsCompact K → Filter.codiscreteWithin K = Filter.cofinite ⊓ Filter.principal K- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 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.
Cites15
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
- Filterstatement · cited by 8,121
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- IsCompactstatement and proof · cited by 1,282
- Filter.principalstatement and proof · cited by 740
- le_imp_le_of_le_of_leproof · cited by 576
- T1Spacestatement and proof · cited by 275
- Filter.cofinitestatement · cited by 251
- Filter.codiscreteWithinstatement and proof · cited by 87
- inf_le_infproof · cited by 54
Cited by1
Results whose statement or proof uses this declaration.
- codiscrete_eq_cofiniteproof · cited by 0