Theorems · Theorem · general topology
IsCompact.inter_of_isOpen
∀ {α : Type u_1} [inst : TopologicalSpace α] [QuasiSeparatedSpace α] {U V : Set α},
IsCompact U → IsCompact V → IsOpen U → IsOpen V → IsCompact (U ∩ V)- Defined in
- Mathlib.Topology.QuasiSeparated
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
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
- IsOpenstatement and proof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- QuasiSeparatedSpacestatement and proof · cited by 49
- QuasiSeparatedSpace.inter_isCompactproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IsCompact.isRetrocompactproof · cited by 4
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2