Homotopy Type Theory directionally differentiable function > history (Rev #2, changes)

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Given a calculus fieldFFsequentially Cauchy complete Archimedean ordered field and a F F \mathbb{R} - and acalculus vector space?real vector space VV, a scalar function f:V F f:V \to F \mathbb{R} is a directionally differentiable function if for every vector v:Vv:V and line L vVL_v \subseteq V,

L v v:V a: Fv=aw L_v \coloneqq \sum_{v:V} \Vert \sum_{a:F} \sum_{a:\mathbb{R}} v = a w \Vert

with canonical equivalence m: FL v m:F m:\mathbb{R} \cong L_v and canonical inclusion i:L vVi:L_v \hookrightarrow V, the composite fimf \circ i \circ m is a differentiable function.

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Revision on June 10, 2022 at 14:32:09 by Anonymous?. See the history of this page for a list of all contributions to it.