Definition:Open


 * Topology:
 * Open set: A set $U$ in a topological space $\left({S, \tau}\right)$ such that $U \in \tau$.
 * Open mapping: A mapping $f: T_1 \to T_2$ from a topological space $T_1$ to another $T_2$ which maps open sets in $T_1$ to open sets in $T_2$.
 * Open cover: A cover consisting of open sets.
 * Open neighborhood: A neighborhood which is an open set.


 * Metric spaces:
 * Open set: A set $U$ in a metric space $\left({A, d}\right)$ such that every point in $U$ has an open $\epsilon$-ball lying entirely within $U$.
 * Open $\epsilon$-ball: the set of points of a metric space within $\epsilon \in \R_{>0}$ distance of a given point.


 * Complex Analysis:
 * Open set: A subset $U$ of the complex plane $\C$ such that every point in $U$ has a neighborhood lying entirely within $U$.


 * Real Analysis:
 * Open interval: A real interval which does not include its endpoints.