Meaning of differentiable manifold | Babel Free

Definitions

1. A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;
2. A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus; (more formally) a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).
3. a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).

Examples

“The charts (homeomorphisms) that make up any differentiable structure of a differentiable manifold are required to be such that the transition from one to another is differentiable.”

“Whitney showed that a differentiable manifold Mᵏ can be regularly mapped on the vector space R#123;2k#125;.”

“The phase space of a dynamical system will be taken to be a differentiable manifold.”

“In this chapter we introduce differentiable manifolds and smooth maps. A differentiable manifold' is a topological space on which there are defined coordinates allowing basic notions of differentiability.”

CEFR level