Theorems · Definition · functional analysis

HasStrictFDerivAt

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : AddCommGroup E] →
        [inst_2 : Module 𝕜 E] →
          [inst_3 : TopologicalSpace E] →
            {F : Type u_3} →
              [inst_4 : AddCommGroup F] →
                [inst_5 : Module 𝕜 F] → [inst_6 : TopologicalSpace F] → (E → F) → (E →L[𝕜] F) → E → Prop

A function f has derivative f' at a in the sense of strict differentiability if f x - f y - f' (x - y) = o(x - y) as x, y → a. This form of differentiability is required, e.g., by the inverse function theorem. Any C^1 function on a vector space over ℝ is strictly differentiable but this definition works, e.g., for vector spaces over p-adic numbers.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

261 results in Mathlib

Foundations

Depth 66 from the axioms, rests on 959 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace