Theorems · Theorem · functional analysis
comap_gauge_nhds_zero_le
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} [inst_2 : TopologicalSpace E],
Absorbent ℝ s → Bornology.IsVonNBounded ℝ s → Filter.comap (gauge s) (nhds 0) ≤ nhds 0- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- nhdsstatement and proof · cited by 5,554
- Norm.normproof · cited by 5,413
- Set.preimageproof · cited by 4,946
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
Cited by2
Results whose statement or proof uses this declaration.
- comap_gauge_nhds_zeroproof · cited by 1
- gauge_eq_zeroproof · cited by 1