Definition:Open Neighborhood/Real Analysis
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Definition
Real Numbers
Let $x\in\R$ be a real number.
Let $I \subseteq \R$ be a subset.
Then $I$ is an open neighborhood of $x$ if and only if $I$ is open and $I$ is a neighborhood of $x$.
Real Euclidean Space
Let $n\geq1$ be a natural number.
Let $x\in\R^n$.
Let $I \subseteq \R$ be a subset.
Then $I$ is an open neighborhood of $x$ if and only if $I$ is open and $I$ is a neighborhood of $x$.