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In this chapter we define a smooth function on a manifold. We define the derivation of a smooth function on \(\mathbb {R}^n\) ; we introduce the local co-ordinates of a point p of a manifold. We define the germ of a smooth function at p, and then a tangent vector at p and the tangent space at p.

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Tangent Spaces

  • 章节

  • 发表日期：

    2026年

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  • Will J. Merry

摘要

In this chapter we define a smooth function on a manifold. We define the derivation of a smooth function on \(\mathbb {R}^n\) ; we introduce the local co-ordinates of a point p of a manifold. We define the germ of a smooth function at p, and then a tangent vector at p and the tangent space at p.