Theorems · Theorem · general topology
Disjoint.closure_left
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, Disjoint s t → IsOpen t → Disjoint (closure s) t- Defined in
- Mathlib.Topology.Closure
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 62 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.
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
- IsOpenstatement and proof · cited by 2,400
- Disjointstatement and proof · cited by 2,201
- closurestatement · cited by 1,254
- closure_minimalproof · cited by 94
- Disjoint.mono_leftproof · cited by 50
- IsOpen.isClosed_complproof · cited by 50
- disjoint_compl_leftproof · cited by 17
- Disjoint.subset_compl_rightproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- SeparatedNhds.disjoint_closure_leftproof · cited by 4
- Disjoint.closure_rightproof · cited by 2
- MeasureTheory.measurableSet_range_of_continuous_injectiveproof · cited by 1
- hasSeparatingCovers_iff_separatedNhdsproof · cited by 1
- ExtremallyDisconnected.disjoint_closure_of_disjoint_isOpenproof · cited by 0
- isNowhereDense_iff_disjointproof · cited by 0