Definition:Open

Disambiguation

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Open may refer to:

• 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.