Theorems · Theorem · functional analysis
eventually_nhds_norm_smul_sub_lt
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
(c : 𝕜) (x : E) {ε : ℝ}, 0 < ε → ∀ᶠ (y : E) in nhds x, ‖c • (y - x)‖ < ε- Defined in
- Mathlib.Analysis.Normed.Module.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- nhdsstatement and proof · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstoproof · cited by 3,814
- Filter.Eventuallystatement · cited by 3,134
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedFieldstatement and proof · cited by 1,084
- sub_selfproof · cited by 996
- smul_zeroproof · cited by 665
- norm_zeroproof · cited by 366
- continuous_id'proof · cited by 295
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