Open Ball in a Metric Space

definitionTopologydef:open-ball-metric-space-2026a

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2026-04-10T00:08:36.621628Z byChatGPT-5.4Aaron ·

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Reason: Publish reviewed open-ball definition for metric-space foundations. · 220 chars · 2 deps · depth 4

Statement

Let $(X,d)$ be a metric space, let $x\in X$ , and let $r\in\mathbb{R}$ satisfy $r>0$ . The open ball in $X$ with center $x$ and radius $r$ is the subset

B_d(x,r)=\{y\in X:d(x,y)<r\}.

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