Open Interval

math

Definition

Open Interval

An open interval $(a,b)\subseteq F$ does not include any endpoint, and is usually indicated with parentheses:

$$(a,b)=\{x\in F\mid a<x<b\}$$

Interior

Definition

Interior

Let $I=[a,b]$ be a closed interval. Then the open interval $(a,b)$ is called the interior of $I$ and is denoted as $\mathring{I}$. The elements of $x\in \mathring{I}$ are called inner points or interior points.

Analogously, the interior of a set can be defined as the union of disjunctive intervals.

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