Theorems · Inductive type · general topology
TopologicalSpace.IrreducibleCloseds
(α : Type u_4) → [TopologicalSpace α] → Type u_4
The type of irreducible closed subsets of a topological space.
- Defined in
- Mathlib.Topology.Sets.Closeds
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by48
Results whose statement or proof uses this declaration.
- TopologicalSpace.IrreducibleCloseds.mapstatement and proof · cited by 8
- topologicalKrullDimproof · cited by 6
- TopologicalSpace.IrreducibleCloseds.carrierstatement and proof · cited by 5
- irreducibleSetEquivPointsstatement and proof · cited by 3
- topologicalKrullDim_zero_of_discreteTopologyproof · cited by 2
- TopologicalSpace.IrreducibleCloseds.equivSubtypestatement and proof · cited by 2
- TopologicalSpace.IrreducibleCloseds.equivSubtype'statement and proof · cited by 2
- TopologicalSpace.IrreducibleCloseds.extstatement and proof · cited by 2
- TopologicalSpace.IrreducibleCloseds.isIrreducible'statement and proof · cited by 2
- PrimeSpectrum.pointsEquivIrreducibleClosedsstatement and proof · cited by 1
- TopologicalSpace.IrreducibleCloseds.isClosedstatement and proof · cited by 1
- TopologicalSpace.IrreducibleCloseds.isClosed'statement and proof · cited by 1