Theorems · Theorem · general topology
isTopologicalBasis_isClopen
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] [CompactSpace X] [TotallyDisconnectedSpace X],
TopologicalSpace.IsTopologicalBasis {s | IsClopen s}- Defined in
- Mathlib.Topology.Separation.Profinite
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 6,101
- nhdsproof · cited by 5,554
- IsOpenproof · cited by 2,400
- T2Spacestatement and proof · cited by 1,351
- CompactSpacestatement and proof · cited by 593
- IsOpen.mem_nhdsproof · cited by 470
- TotallyDisconnectedSpacestatement and proof · cited by 295
- Filter.HasBasis.mem_iffproof · cited by 193
- IsClopenstatement and proof · cited by 189
- TopologicalSpace.IsTopologicalBasisstatement · cited by 126
Cited by5
Results whose statement or proof uses this declaration.
- LightProfinite.epi_iff_surjectiveproof · cited by 3
- compact_exists_isClopen_in_isOpenproof · cited by 3
- Profinite.epi_iff_surjectiveproof · cited by 2
- Profinite.exists_isClopen_of_cofilteredproof · cited by 1
- Stonean.epi_iff_surjectiveproof · cited by 1