Theorems · Theorem · functional analysis
gauge_eq_zero
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} {x : E} [inst_2 : TopologicalSpace E]
[T1Space E], Absorbent ℝ s → Bornology.IsVonNBounded ℝ s → (gauge s x = 0 ↔ x = 0)- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Compl.complproof · cited by 2,925
- absproof · cited by 1,814
- Filter.comapproof · cited by 546
- IsOpen.mem_nhdsproof · cited by 470
Cited by1
Results whose statement or proof uses this declaration.
- gauge_posproof · cited by 4