Theorems · Theorem · general topology
isClosed_sum_iff
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set (X ⊕ Y)},
IsClosed s ↔ IsClosed (Sum.inl ⁻¹' s) ∧ IsClosed (Sum.inr ⁻¹' s)- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Set.preimagestatement and proof · cited by 4,946
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- IsClosedstatement · cited by 1,639
Cited by1
Results whose statement or proof uses this declaration.
- isClosedMap_sumproof · cited by 1