Theorems · Theorem · general topology
IsDenseInducing.dense
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {i : α → β},
IsDenseInducing i → DenseRange iThe range of a dense inducing map is a dense set.
- Defined in
- Mathlib.Topology.DenseEmbedding
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- DenseRangestatement · cited by 164
- IsDenseInducingstatement and proof · cited by 56
Cited by20
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.simpleFunc.denseRangeproof · cited by 10
- IsDenseInducing.comap_nhds_neBotproof · cited by 5
- IsDenseInducing.prodMapproof · cited by 4
- IsDenseInducing.closure_image_mem_nhdsproof · cited by 2
- eventually_residual_liouvilleproof · cited by 2
- map_real_smulproof · cited by 2
- Complex.subfield_eq_of_closedproof · cited by 2
- IsDenseInducing.closure_rangeproof · cited by 1
- IsDenseInducing.dense_imageproof · cited by 1
- IsDenseInducing.extend_Z_bilinproof · cited by 1
- Complex.uniformContinuous_ringHom_eq_id_or_conjproof · cited by 1
- IsDenseInducing.isUniformInducing_extendproof · cited by 1