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Theorems · Theorem · general topology

DenseRange.prodMap

∀ {Y : Type v} {Z : Type u_2} [inst : TopologicalSpace Y] [inst_1 : TopologicalSpace Z] {ι : Type u_5} {κ : Type u_6}
  {f : ι → Y} {g : κ → Z}, DenseRange f → DenseRange g → DenseRange (Prod.map f g)

If f and g are maps with dense range, then Prod.map f g has dense range.

Defined in
Mathlib.Topology.Constructions.SumProd
Cited by
5 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsDenseInducing.prodMap · cited by 4IsDenseInducing.prodMapUniformSpace.Completion.denseRange_coe₂ · cited by 2Completion.denseRange_coe₂isClosed_property2 · cited by 1isClosed_property2isClosed_property3 · cited by 1isClosed_property3UniformSpace.Completion.denseRange_coe₃ · cited by 1Completion.denseRange_coe₃TopologicalSpace · cited by 24529TopologicalSpaceDense · cited by 359DenseDenseRange · cited by 164DenseRangeDense.prod · cited by 3Dense.prodSet.prod_range_range_eq · cited by 2Set.prod_range_range_eqDenseRange.prodMapCITED BYCITES

Cites5

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Cited by5

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