Theorems · Theorem · general topology
topologicalKrullDim_zero_of_discreteTopology
∀ (X : Type u_3) [inst : TopologicalSpace X] [DiscreteTopology X], topologicalKrullDim X ≤ 0
- Defined in
- Mathlib.Topology.KrullDimension
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- ENatstatement · cited by 4,985
- WithBotstatement · cited by 1,498
- Eq.leproof · cited by 605
- DiscreteTopologystatement and proof · cited by 373
- LE.le.antisymm'proof · cited by 104
- TopologicalSpace.IrreducibleClosedsproof · cited by 30
- IsIrreducible.isPreirreducibleproof · cited by 7
- IsIrreducible.nonemptyproof · cited by 7
- DiscreteTopology.isDiscreteproof · cited by 7
- topologicalKrullDimstatement · cited by 6
- TopologicalSpace.IrreducibleCloseds.carrierproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isLocallyArtinianScheme_Specproof · cited by 0