Theorems · Theorem · general topology
nhds_prod_eq
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {x : X} {y : Y},
nhds (x, y) = nhds x ×ˢ nhds y- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 84 results in Mathlib
- Foundations
- Depth 69 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- SProd.sprodstatement · cited by 1,750
- Filter.comapproof · cited by 546
- nhds_inducedproof · cited by 32
- Filter.prod_eq_infproof · cited by 4
- nhds_infproof · cited by 2
Cited by84
Results whose statement or proof uses this declaration.
- Filter.Tendsto.prodMk_nhdsproof · cited by 46
- IsCompact.prodproof · cited by 26
- isUniformAddGroup_of_addCommGroupproof · cited by 21
- MeasureTheory.StronglyMeasurable.prodMkproof · cited by 11
- Filter.HasBasis.prod_nhdsproof · cited by 9
- IsProperMap.prodMapproof · cited by 7
- Topology.IsInducing.prodMapproof · cited by 7
- nhdsWithin_prod_eqproof · cited by 7
- cauchy_nhdsproof · cited by 7
- IsOpenMap.prodMapproof · cited by 6
- IsCompact.nhdsSet_prod_eqproof · cited by 5
- hasStrictFDerivAt_uncurry_coprodproof · cited by 5