Theorems · Definition · functional analysis

DifferentiableWithinAt

(𝕜 : Type u_1) →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : AddCommGroup E] →
        [Module 𝕜 E] →
          [TopologicalSpace E] →
            {F : Type u_3} →
              [inst_4 : AddCommGroup F] → [Module 𝕜 F] → [TopologicalSpace F] → (E → F) → Set E → E → Prop

A function f is differentiable at a point x within a set s if it admits a derivative there (possibly non-unique).

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

453 results in Mathlib

Foundations

Depth 61 from the axioms, rests on 890 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace