Theorems · Theorem · general topology
WithZeroTopology.singleton_mem_nhds_of_ne_zero
∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] {γ : Γ₀}, γ ≠ 0 → {γ} ∈ nhds γIf γ is a nonzero element of a linearly ordered group with zero element adjoined, then {γ}
is a neighbourhood of γ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- WithZeroTopology.topologicalSpacestatement · cited by 27
- WithZeroTopology.nhds_of_ne_zeroproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Valued.closure_coe_completion_v_ltproof · cited by 1