Theorems · Theorem · general topology
hasSmallInductiveDimensionLT_zero_iff
∀ {X : Type u_1} [inst : TopologicalSpace X], HasSmallInductiveDimensionLT X 0 ↔ IsEmpty X- Defined in
- Mathlib.Topology.SmallInductiveDimension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- IsEmptystatement and proof · cited by 759
- frontierproof · cited by 214
- TopologicalSpace.IsTopologicalBasisproof · cited by 126
- HasSmallInductiveDimensionLTstatement and proof · cited by 9
- HasSmallInductiveDimensionLT.casesOnproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- HasSmallInductiveDimensionLT_zero_iffproof · cited by 0