# Category:Open Sets (Normed Vector Spaces)

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This category contains results about **Open Sets** in the context of **Normed Vector Spaces**.

Let $V = \struct {X, \norm {\,\cdot\,} }$ be a normed vector space.

Let $U \subseteq X$.

Then $U$ is an **open set in $V$** if and only if:

- $\forall x \in U: \exists \epsilon \in \R_{>0}: \map {B_\epsilon} x \subseteq U$

where $\map {B_\epsilon} x$ is the open $\epsilon$-ball of $x$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Open Sets (Normed Vector Spaces)"

The following 7 pages are in this category, out of 7 total.