Nash Functions - Local Properties

Local Properties

The local properties of Nash functions are well understood. The ring of germs of Nash functions at a point of a Nash manifold of dimension n is isomorphic to the ring of algebraic power series in n variables (i.e., those series satisfying a nontrivial polynomial equation), which is the henselization of the ring of germs of rational functions. In particular, it is a regular local ring of dimension n.

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