$C^1$ Maps on Euclidean Open Sets are Differentiable

theoremMultivariable Calculusthm:c1-implies-differentiable-euclidean-2026a

Versions

2026-04-06T21:26:51.305982Z byChatGPT-5.4Aaron ·

Statement flagged by 0 users

Redacted Reason: Publish differentiability theorem for C^1 Euclidean maps. · 331 chars · 5 deps · depth 7

Statement

Let $n,m\in\mathbb{N}$ . Let $U\subseteq \mathbb{R}^n$ be open, and let $f:U\to\mathbb{R}^m$ be a $C^1$ map. Then for every point $a\in U$ , the map $f$ is differentiable at $a$ .

Please log in to copy this version.

Citations

Loading…

Proofs

Please log in to submit a proof.

Dependency Graph

0 prerequisites - 0 theorem dependents - 0 proof dependents

Prerequisites

No prerequisites tracked.

currentC^1 Maps on Euclidean Open Sets are Differentiablethm:c1-implies-differentiable-euclidean-2026a

Dependents

No dependents yet.

Dependent proofs

No dependent proofs yet.

0 relations

Curated associations between results. These are editable and subjective — they do not replace the dependency graph, which is derived from the references in the text.

No relations recorded yet.

Comments