Theorems · Definition · general topology
TopologicalSpace.denseSeq
(α : Type u) → [t : TopologicalSpace α] → [TopologicalSpace.SeparableSpace α] → [Nonempty α] → ℕ → α
A dense sequence in a non-empty separable topological space.
If α might be empty, then TopologicalSpace.exists_countable_dense is the main way to use
separability of α.
- Defined in
- Mathlib.Topology.Bases
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- TopologicalSpace.exists_dense_seqproof · cited by 5
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.approxOnproof · cited by 39
- MeasureTheory.SimpleFunc.tendsto_approxOnproof · cited by 6
- Metric.PiNatEmbed.distDenseSeqproof · cited by 6
- TopologicalSpace.denseRange_denseSeqstatement · cited by 5
- MeasureTheory.SimpleFunc.approxOn_memproof · cited by 3
- MeasureTheory.SimpleFunc.edist_approxOn_monoproof · cited by 2
- Metric.PiNatEmbed.separationproof · cited by 2
- MeasureTheory.exists_isCompact_closure_measure_compl_ltproof · cited by 1
- Metric.PiNatEmbed.continuous_distDenseSeqproof · cited by 1
- WeakDual.exists_countable_separatingproof · cited by 1
- ProbabilityTheory.strong_law_ae_of_measurableproof · cited by 1
- TopologicalSpace.denseSeq.congr_simpstatement and proof · cited by 0