Definition:Open Neighborhood/Real Analysis

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 $x$.