Theorems · Theorem · general topology
SeparatedNhds.of_isCompact_isCompact
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {s t : Set X},
IsCompact s → IsCompact t → Disjoint s t → SeparatedNhds s t- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
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
- IsOpenproof · cited by 2,400
- Disjointstatement and proof · cited by 2,201
- T2Spacestatement and proof · cited by 1,351
- IsCompactstatement and proof · cited by 1,282
- IsClosed.isOpen_complproof · cited by 126
- SeparatedNhdsstatement · cited by 33
- generalized_tube_lemmaproof · cited by 6
- Set.prod_subset_compl_diagonal_iff_disjointproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.isOpen_setOfPred_disjoint_coeproof · cited by 3
- SeparatedNhds.of_finset_finsetproof · cited by 2