Theorems · Theorem · general topology
IsDenseInducing.isInducing
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {i : α → β},
IsDenseInducing i → Topology.IsInducing i- Defined in
- Mathlib.Topology.DenseEmbedding
- Cited by
- 9 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
- Topology.IsInducingstatement · cited by 266
- IsDenseInducingstatement and proof · cited by 56
- IsDenseInducing.toIsInducingproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- IsDenseInducing.nhds_eq_comapproof · cited by 7
- IsDenseInducing.prodMapproof · cited by 4
- IsDenseInducing.continuousproof · cited by 4
- IsDenseEmbedding.subtypeproof · cited by 3
- Valued.continuous_extensionproof · cited by 2
- IsDenseInducing.dense_imageproof · cited by 1
- uniform_extend_subtypeproof · cited by 0
- Filter.HasBasis.hasBasis_of_isDenseInducingproof · cited by 0
- IsDenseInducing.extend_eq'proof · cited by 0