Theorems · Theorem · general topology
IsClosed.prod
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s₁ : Set X} {s₂ : Set Y},
IsClosed s₁ → IsClosed s₂ → IsClosed (s₁ ×ˢ s₂)- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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
- SProd.sprodstatement and proof · cited by 1,750
- IsClosedstatement and proof · cited by 1,639
- IsClosed.closure_eqproof · cited by 139
- closure_eq_iff_isClosedproof · cited by 12
- closure_prod_eqproof · cited by 10
Cited by10
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.prodMapproof · cited by 1
- CompactT2.Projective.extremallyDisconnectedproof · cited by 1
- t2Space_of_properSMul_of_t1Groupproof · cited by 0
- t2Space_of_properVAdd_of_t1AddGroupproof · cited by 0
- IsClopen.prodproof · cited by 0
- ContinuousLinearMap.closed_complemented_range_of_isCompl_of_ker_eq_botproof · cited by 0
- isClosedMap_prodMk_leftproof · cited by 0
- isClosedMap_prodMk_rightproof · cited by 0