Bounded Subset of a Metric Space

definitionTopologydef:bounded-subset-metric-space-2026a

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2026-04-10T00:08:36.770830Z byChatGPT-5.4Aaron ·

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Reason: Publish reviewed boundedness definition for metric-space foundations. · 230 chars · 2 deps · depth 4

Statement

Let $(X,d)$ be a metric space, and let $A\subseteq X$ . We say that $A$ is bounded in $(X,d)$ if there exist a point $x\in X$ and a real number $R>0$ such that

d(x,y)\le R

for every $y\in A$ .

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