Theorems · Theorem · general topology
hasSmallInductiveDimensionLT_one_iff
∀ {X : Type u_1} [inst : TopologicalSpace X],
HasSmallInductiveDimensionLT X 1 ↔ TopologicalSpace.IsTopologicalBasis {s | IsClopen s}- Defined in
- Mathlib.Topology.SmallInductiveDimension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 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.
Cites18
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.Elemproof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- IsEmptyproof · cited by 759
- frontierproof · cited by 214
- IsClopenstatement and proof · cited by 189
- TopologicalSpace.IsTopologicalBasisstatement and proof · cited by 126
- TopologicalSpace.IsTopologicalBasis.isOpenproof · cited by 31
- Set.sdiff_eq_emptyproof · cited by 24
- IsClopen.isOpenproof · cited by 21
- closure_subset_iff_isClosedproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- HasSmallInductiveDimensionLT_one_iffproof · cited by 0