Theorems · Theorem · general topology
SeparatedNhds.isOpen_left_of_isOpen_union
∀ {X : Type u_1} [inst : TopologicalSpace X] {s t : Set X}, SeparatedNhds s t → IsOpen (s ∪ t) → IsOpen s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 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.
Cites12
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
- Disjointproof · cited by 2,201
- Disjoint.symmproof · cited by 125
- IsOpen.interproof · cited by 98
- Set.union_emptyproof · cited by 78
- Disjoint.mono_leftproof · cited by 50
- Set.inter_eq_leftproof · cited by 44
- SeparatedNhdsstatement and proof · cited by 33
- Set.union_inter_distrib_rightproof · cited by 28
- Disjoint.inter_eqproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- SeparatedNhds.isOpen_right_of_isOpen_unionproof · cited by 1
- SeparatedNhds.isOpen_union_iffproof · cited by 0