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Theorems · Theorem · general topology

Set.Subsingleton.isPreirreducible

∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, s.Subsingleton → IsPreirreducible s
Defined in
Mathlib.Topology.Irreducible
Cited by
4 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
TopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsPreirreducible.preimage · cited by 2IsPreirreducible.preimageisPreirreducible_singleton · cited by 2isPreirreducible_singletonpreimage_mem_irreducibleComponents · cited by 1preimage_mem_irreducibleC…IsIrreducible.preimage · cited by 0IsIrreducible.preimageSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Nonempty · cited by 2627Set.NonemptyIsOpen · cited by 2400IsOpenSet.Subsingleton · cited by 276Set.SubsingletonIsPreirreducible · cited by 43IsPreirreducibleSubsingleton.isPreirreducibleCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.