Theorems · Theorem · general topology
WithZeroTopology.nhds_coe_units
∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] (γ : Γ₀ˣ), nhds ↑γ = pure ↑γThe neighbourhood filter of an invertible element consists of all sets containing that element.
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- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Units.ne_zeroproof · cited by 68
- WithZeroTopology.topologicalSpacestatement · cited by 27
- WithZeroTopology.nhds_of_ne_zeroproof · cited by 8
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