# Definition:Open

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## Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

**Open** may refer to:

- Predicate Logic: an open statement is a statement which contains at least one free occurrence of a variable.

- 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.
- Open Set

- Open question: another term for a hypothesis: a statement whose truth value is unknown.