Theorems · Theorem · general topology
IsOpen.closure_inter
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsOpen t → closure s ∩ t ⊆ closure (s ∩ t)- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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
- closurestatement and proof · cited by 1,254
- Set.inter_commproof · cited by 291
- IsOpen.inter_closureproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- LocallyFinite.closureproof · cited by 5
- stronglyMeasurable_derivWithin_Iciproof · cited by 2