Theorems · Theorem · functional analysis
tendsto_gauge_nhds_zero_nhdsGE
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} [inst_2 : TopologicalSpace E]
[ContinuousSMul ℝ E], s ∈ nhds 0 → Filter.Tendsto (gauge s) (nhds 0) (nhdsWithin 0 (Set.Ici 0))- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- LT.lt.leproof · cited by 2,189
- nhdsWithinstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_gauge_nhds_zeroproof · cited by 4