Theorems · Theorem · general topology
IsCompact.inter
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {s t : Set X}, IsCompact s → IsCompact t → IsCompact (s ∩ t)- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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.
Cites6
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
- T2Spacestatement and proof · cited by 1,351
- IsCompactstatement and proof · cited by 1,282
- IsCompact.isClosedproof · cited by 77
- IsCompact.inter_rightproof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- IsRetrocompact.interproof · cited by 1