Theorems · Theorem · general topology
WithZeroTopology.isOpen_iff
∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] {s : Set Γ₀}, IsOpen s ↔ 0 ∉ s ∨ ∃ γ, γ ≠ 0 ∧ Set.Iio γ ⊆ s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsOpenstatement · cited by 2,400
- Set.Iiostatement and proof · cited by 1,166
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Filter.HasBasis.mem_iffproof · cited by 193
- isOpen_iff_mem_nhdsproof · cited by 48
- WithZeroTopology.topologicalSpacestatement · cited by 27
- WithZeroTopology.nhds_of_ne_zeroproof · cited by 8
- and_forall_neproof · cited by 6
- WithZeroTopology.hasBasis_nhds_zeroproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- WithZeroTopology.isOpen_Iioproof · cited by 0