Theorems · Theorem · functional analysis
gauge_pos
∀ {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 → (0 < gauge s x ↔ x ≠ 0)- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- T1Spacestatement and proof · cited by 275
- Bornology.IsVonNBoundedstatement and proof · cited by 136
- gaugestatement · cited by 85
- Absorbentstatement and proof · cited by 60
- LE.le.lt_iff_ne'proof · cited by 16
- gauge_nonnegproof · cited by 8
- gauge_eq_zeroproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- gauge_gaugeRescaleproof · cited by 1
- gaugeRescale_self_applyproof · cited by 1
- continuous_gaugeRescaleproof · cited by 0
- gaugeRescale_gaugeRescaleproof · cited by 0