tags:definition |topology

Metric Open Set

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Statements

Definition. (@Eck23, Definition 1.1) Let $(X,d)$ be a metric space. A subset of $S$ is said to be open in $X$ if, for every $s\in S$, there exists $\epsilon >0$ such that the open ball $B_{<\epsilon }(x)$ satisfies $B_{<\epsilon }(s)\subseteq S$.

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