Theorems · Theorem · general topology
genericPoints.finite
∀ {α : Type u_1} [inst : TopologicalSpace α] [T0Space α], (irreducibleComponents α).Finite → (genericPoints α).Finite- Defined in
- Mathlib.Topology.Sober
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT0Space
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Finitestatement and proof · cited by 1,814
- T0Spacestatement and proof · cited by 179
- irreducibleComponentsstatement and proof · cited by 35
- Finite.of_injectiveproof · cited by 32
- genericPointsstatement · cited by 10
- genericPoints.componentproof · cited by 7
- genericPoints.component_injectiveproof · cited by 2
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