Theorems · Theorem · general topology
smallInductiveDimension_eq_bot
∀ {X : Type u_1} [inst : TopologicalSpace X], smallInductiveDimension X = ⊥ ↔ IsEmpty X- Defined in
- Mathlib.Topology.SmallInductiveDimension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderproof · cited by 7,952
- ENatstatement and proof · cited by 4,985
- Bot.botstatement and proof · cited by 4,720
- Nat.cast_zeroproof · cited by 1,870
- WithBotstatement and proof · cited by 1,498
- OrderBotproof · cited by 1,055
- IsEmptystatement · cited by 759
- WithBot.someproof · cited by 541
- bot_eq_zero'proof · cited by 92
- smallInductiveDimensionstatement and proof · cited by 7
- WithBot.lt_coe_botproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- smallInductiveDimension_of_isEmptyproof · cited by 0