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Theorems · Theorem · general topology

genericPoints.component_ofComponent

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : QuasiSober α] (x : ↑(irreducibleComponents α)),
  genericPoints.component (genericPoints.ofComponent x) = x
Defined in
Mathlib.Topology.Sober
Cited by
2 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceQuasiSober
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Around this declaration

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

genericPoints.equiv · cited by 2genericPoints.equivgenericPoints.ofComponent_component · cited by 0genericPoints.ofComponent…genericPoints.component_surjective · cited by 0genericPoints.component_s…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemirreducibleComponents · cited by 35irreducibleComponentsQuasiSober · cited by 31QuasiSobergenericPoints.component · cited by 7genericPoints.componentgenericPoints.ofComponent · cited by 6genericPoints.ofComponentgenericPoints.isGenericPoint_ofComponent · cited by 2genericPoints.isGenericPo…genericPoints.component_ofCom…CITED BYCITES

Cites8

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Cited by3

Results whose statement or proof uses this declaration.