Theorems · Theorem · general topology
IsDenseEmbedding.isDenseInducing
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {e : α → β},
IsDenseEmbedding e → IsDenseInducing e- Defined in
- Mathlib.Topology.DenseEmbedding
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- IsDenseInducingstatement · cited by 56
- IsDenseEmbeddingstatement and proof · cited by 24
- IsDenseEmbedding.toIsDenseInducingproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Rat.interior_compact_eq_emptyproof · cited by 1
- MeasureTheory.Lp.simpleFunc.isDenseInducingproof · cited by 1
- IsDenseEmbedding.separableSpaceproof · cited by 0
- CauchyFilter.nonempty_cauchyFilter_iffproof · cited by 0
- IsDenseEmbedding.dense_imageproof · cited by 0
- IsDenseEmbedding.prodMapproof · cited by 0