Theorems · Theorem · general topology
TopologicalSpace.exists_countable_dense
∀ (α : Type u) [t : TopologicalSpace α] [TopologicalSpace.SeparableSpace α], ∃ s, s.Countable ∧ Dense s
- Defined in
- Mathlib.Topology.Bases
- Cited by
- 15 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Countablestatement · cited by 545
- Densestatement · cited by 359
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- TopologicalSpace.SeparableSpace.exists_countable_denseproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- TopologicalSpace.exists_dense_seqproof · cited by 5
- Dense.exists_countable_dense_subsetproof · cited by 2
- stronglyMeasurable_derivWithin_Iciproof · cited by 2
- KuratowskiEmbedding.exists_isometric_embeddingproof · cited by 2
- DenseRange.separableSpaceproof · cited by 2
- IsClosed.two_pow_mk_lt_continuumproof · cited by 1
- IsOpenMap.separableSpace_of_injectiveproof · cited by 1
- Pairwise.countable_of_isOpen_disjointproof · cited by 1
- exists_countable_upperSemicontinuous_isGLBproof · cited by 1
- measurable_iSup_of_lowerSemicontinuousproof · cited by 1
- LipschitzWith.ae_differentiableAt_of_realproof · cited by 1
- TopologicalSpace.Compacts.separableSpace_iffproof · cited by 1