Theorems · Theorem · general topology
IsCompact.closure_eq_biUnion_inseparable
∀ {X : Type u_1} [inst : TopologicalSpace X] [R1Space X] {K : Set X},
IsCompact K → closure K = ⋃ x ∈ K, {y | Inseparable x y}- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceR1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.ofPredstatement · cited by 6,101
- Set.iUnionstatement · cited by 2,483
- Set.extproof · cited by 2,266
- IsCompactstatement and proof · cited by 1,282
- closurestatement · cited by 1,254
- Inseparablestatement and proof · cited by 160
- R1Spacestatement and proof · cited by 125
- IsCompact.mem_closure_iff_exists_inseparableproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IsCompact.closure_subset_of_isOpenproof · cited by 9
- IsCompact.closure_subset_measurableSetproof · cited by 4
- IsCompact.closure_eq_biUnion_closure_singletonproof · cited by 0