Theorems · Inductive type · general topology
FirstCountableTopology
(α : Type u) → [t : TopologicalSpace α] → Prop
A first-countable space is one in which every point has a countable neighborhood basis.
- Defined in
- Mathlib.Topology.Bases
- Cited by
- 106 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by108
Results whose statement or proof uses this declaration.
- exists_seq_strictAnti_tendstostatement and proof · cited by 18
- exists_seq_strictAnti_tendsto'statement and proof · cited by 10
- exists_seq_strictMono_tendsto'statement and proof · cited by 6
- IsCompact.isSeqCompactstatement and proof · cited by 6
- MeasureTheory.IsStoppingTime.measurableSet_eqstatement and proof · cited by 5
- MeasureTheory.IsStoppingTime.measurableSet_eq'statement and proof · cited by 5
- ae_le_essSupstatement and proof · cited by 4
- IsCompact.tendsto_subseqstatement and proof · cited by 4
- eventually_le_limsupstatement and proof · cited by 4
- limsup_eq_botstatement and proof · cited by 3
- exists_seq_strictMono_tendstostatement and proof · cited by 3
- MeasureTheory.tendsto_measure_biInter_gtstatement and proof · cited by 3