Theorems · Theorem · general topology
HasSmallInductiveDimensionLT_one_iff
Deprecated since 2026-06-21Use hasSmallInductiveDimensionLT_one_iff instead.
∀ {X : Type u_1} [inst : TopologicalSpace X],
HasSmallInductiveDimensionLT X 1 ↔ TopologicalSpace.IsTopologicalBasis {s | IsClopen s}Alias of hasSmallInductiveDimensionLT_one_iff.
- Defined in
- Mathlib.Topology.SmallInductiveDimension
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- Set.ofPredstatement · cited by 6,101
- IsClopenstatement · cited by 189
- TopologicalSpace.IsTopologicalBasisstatement · cited by 126
- HasSmallInductiveDimensionLTstatement · cited by 9
- hasSmallInductiveDimensionLT_one_iffproof · cited by 1
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