Category:Open Sets (Metric Spaces)
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This category contains results about Open Sets in the context of Metric Spaces.
Let $M = \struct {A, d}$ be a metric space.
Let $U \subseteq A$.
Then $U$ is an open set in $M$ if and only if it is a neighborhood of each of its points.
That is:
- $\forall y \in U: \exists \epsilon \in \R_{>0}: \map {B_\epsilon} y \subseteq U$
where $\map {B_\epsilon} y$ is the open $\epsilon$-ball of $y$.
Pages in category "Open Sets (Metric Spaces)"
This category contains only the following page.