Theorems · Theorem · general topology
closure_prod_eq
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X} {t : Set Y},
closure (s ×ˢ t) = closure s ×ˢ closure t- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.extproof · cited by 2,266
- nhdsWithinproof · cited by 1,912
- SProd.sprodstatement and proof · cited by 1,750
- closurestatement and proof · cited by 1,254
- Filter.NeBotproof · cited by 853
- nhdsWithin_prod_eqproof · cited by 7
Cited by10
Results whose statement or proof uses this declaration.
- IsClosed.prodproof · cited by 10
- map_mem_closure₂proof · cited by 5
- UniqueDiffWithinAt.prodproof · cited by 4
- frontier_prod_eqproof · cited by 3
- Dense.prodproof · cited by 3
- hasFDerivWithinAt_closure_of_tendsto_fderivproof · cited by 2
- Complex.closure_reProdImproof · cited by 2
- subset_tangentConeAt_prod_leftproof · cited by 1
- subset_tangentConeAt_prod_rightproof · cited by 1
- TopologicalSpace.IsSeparable.prodproof · cited by 1