Theorems · Theorem · general topology
Metric.PiNatEmbed.injective_distDenseSeq
∀ {X : Type u_3} [inst : MetricSpace X] [inst_1 : TopologicalSpace.SeparableSpace X] (x y : X),
x ≠ y → ∃ n, Metric.PiNatEmbed.distDenseSeq X n x ≠ Metric.PiNatEmbed.distDenseSeq X n y- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement · cited by 25,697
- Set.Elemstatement and proof · cited by 7,166
- nhdsproof · cited by 5,554
- Compl.complproof · cited by 2,925
- MetricSpacestatement and proof · cited by 1,684
- unitIntervalstatement and proof · cited by 607
- Filter.comapproof · cited by 546
- IsOpen.mem_nhdsproof · cited by 470
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- isOpen_compl_singletonproof · cited by 27
- Metric.PiNatEmbed.distDenseSeqstatement and proof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Metric.PiNatEmbed.continuous_distDenseSeq_invproof · cited by 1
- Metric.PiNatEmbed.exists_embedding_to_hilbert_cubeproof · cited by 1