- Thread starter
- #1

- Mar 10, 2012

- 834

Can someone please check if these definitions are correct.

**Definition.**

Let $U$ be a subset of the real numbers. A function $f:U\to\mathbb R$ is said to be a

*real analytic function*if $f$ has a Taylor series about each point $x\in U$ that converges to the function $f$ in an open neighborhood of $x$.

**Definition.**

Let $U$ be a subset of real numbers and $f:U\to\mathbb R^n$ be a function. Write $f(x)=(f_1(x),\ldots,f_n(x))$. Then $f$ is said to be a

*real analytic curve*if each $f_i$ is are analytic.