Definition:Open


 * Topology:
 * A set $U$ in a topological space $\left({X, \vartheta}\right)$ is open iff $U \in \vartheta$.
 * A mapping $f: X \to Y$ from a topological space $X$ to another $Y$ is open iff it maps open sets in $X$ to open sets in $Y$.
 * An open cover is a cover consisting of open sets.
 * An open neighborhood is a neighborhood which is an open set.


 * Metric spaces:
 * A set $U$ in a metric space $\left({X, d}\right)$ is open iff every point in $U$ has a neighborhood lying entirely within $U$.


 * Complex Analysis:
 * A subset $U$ of the complex plane $\C$ is open iff every point in $U$ has a neighborhood lying entirely within $U$.


 * Real Analysis:
 * An open interval is a real interval which does not include its endpoints.