Theorems · Theorem · general topology
SeparatedNhds.isClosed_left_of_isClosed_union
∀ {X : Type u_1} [inst : TopologicalSpace X] {s t : Set X}, SeparatedNhds s t → IsClosed (s ∪ t) → IsClosed s- Cited by
- 2 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.
Cites20
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
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- Disjointproof · cited by 2,201
- IsClosedstatement and proof · cited by 1,639
- compl_complproof · cited by 229
- Set.union_emptyproof · cited by 78
- isOpen_compl_iffproof · cited by 63
- Disjoint.mono_leftproof · cited by 50
- disjoint_compl_rightproof · cited by 47
- SeparatedNhdsstatement and proof · cited by 33
Cited by2
Results whose statement or proof uses this declaration.
- SeparatedNhds.isClosed_right_of_isClosed_unionproof · cited by 1
- SeparatedNhds.isClosed_union_iffproof · cited by 0