Function continuous at a point

This article defines a property that can be evaluated for a function on a (particular kind of) set, and a point in that set. A function satisfying the property at every point, it is termed a continuous function
View other properties of functions at points

Definition

On a domain in the complex numbers

Let $U$ be an open subset of $\mathbb {C}$ and $f:U\to \mathbb {C}$ be a function. Suppose $z_{0}\in U$ is a point. We say that $f$ is continuous at $z_{0}$ if there exists an open subset $V\ni z_{0}$ such that the restriction of $f$ to $V$ is continuous.