CompletelyRegularSpace.of_isTopologicalBasis_clopens

∀ {X : Type u} [inst : TopologicalSpace X],
  TopologicalSpace.IsTopologicalBasis {s | IsClopen s} → CompletelyRegularSpace X

Defined in: Mathlib.Topology.Separation.CompletelyRegular
Cited by: 0 results in Mathlib
Foundations: Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Set.ofPredstatement and proof · cited by 6,101
Compl.complproof · cited by 2,925
IsClosedproof · cited by 1,639
Set.indicatorproof · cited by 723
continuous_constproof · cited by 278
IsClopenstatement and proof · cited by 189
Set.indicator_of_memproof · cited by 161
TopologicalSpace.IsTopologicalBasisstatement and proof · cited by 126
IsClosed.isOpen_complproof · cited by 126
TopologicalSpace.IsTopologicalBasis.exists_subset_of_mem_openproof · cited by 58

Results whose statement or proof uses this declaration.

Nothing cites this yet.