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.