regular function

《incompressible-fluid-equations》 · 第 19 页 · Lecture 2「Regular Functions and Maps」

Let $U\subseteq X$ be any open set and $p\in U$ any point. We say that a function $f$ on $U$ is regular at $p$ if in some neighborhood $V$ of $p$ it is expressible as a quotient $g/h$, where $g$ and $h\in K[z_1,\ldots,z_n]$ are polynomials and $h(p)\ne0$. We say that $f$ is regular on $U$ if it is regular at every point of $U$.