Theorems · Theorem · global analysis
mem_tangentConeAt_of_pow_smul
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] {s : Set E} {x y : E} {r : 𝕜},
r ≠ 0 → ‖r‖ < 1 → (∀ᶠ (n : ℕ) in Filter.atTop, x + r ^ n • y ∈ s) → y ∈ tangentConeAt 𝕜 s x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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 · 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
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- ContinuousSMulstatement and proof · cited by 1,016
- NormedDivisionRingstatement and proof · cited by 360
- tangentConeAtstatement · cited by 54
- tendsto_nhdsWithin_iffproof · cited by 37
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