Theorems · Inductive type · general topology
TotallySeparatedSpace
(α : Type u) → [TopologicalSpace α] → Prop
A space is totally separated if any two points can be separated by two disjoint open sets covering the whole space.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 1 from the axioms · 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 by11
Results whose statement or proof uses this declaration.
- totallySeparatedSpace_of_t0_of_basis_clopenstatement · cited by 2
- exists_isClopen_of_totally_separatedstatement and proof · cited by 2
- TotallySeparatedSpace.casesOnstatement and proof · cited by 1
- totallySeparatedSpace_iffstatement and proof · cited by 1
- totallySeparatedSpace_iff_exists_isClopenstatement · cited by 1
- TotallySeparatedSpace.isTotallySeparated_univstatement and proof · cited by 0
- Set.Countable.totallySeparatedSpacestatement · cited by 0
- loc_compact_t2_tot_disc_iff_tot_sepstatement · cited by 0
- TotallySeparatedSpace.recOnstatement and proof · cited by 0
- CompletelyRegularSpace.totallySeparatedSpace_of_cardinalMk_lt_continuumstatement · cited by 0
- LocallyConstant.separatesPoints_range_toContinuousMapAlgHomstatement and proof · cited by 0