Theorems · Theorem · general topology
genericPoints_eq_singleton
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : QuasiSober α] [inst_2 : IrreducibleSpace α] [T0Space α],
genericPoints α = {genericPoint α}- Defined in
- Mathlib.Topology.Sober
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredproof · cited by 6,101
- Set.univproof · cited by 3,945
- Set.extproof · cited by 2,266
- closureproof · cited by 1,254
- T0Spacestatement and proof · cited by 179
- IrreducibleSpacestatement and proof · cited by 40
- QuasiSoberstatement and proof · cited by 31
- genericPointstatement and proof · cited by 15
- genericPointsstatement · cited by 10
- genericPoint_specproof · cited by 7
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