Theorems · Theorem · general topology
SeparatedNhds.isClosed_right_of_isClosed_union
∀ {X : Type u_1} [inst : TopologicalSpace X] {s t : Set X}, SeparatedNhds s t → IsClosed (s ∪ t) → IsClosed t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 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.
Cites7
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
- IsClosedstatement and proof · cited by 1,639
- Set.union_commproof · cited by 99
- SeparatedNhdsstatement and proof · cited by 33
- SeparatedNhds.symmproof · cited by 6
- SeparatedNhds.isClosed_left_of_isClosed_unionproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SeparatedNhds.isClosed_union_iffproof · cited by 0