Metric Open Sets Form a Topology

theoremTopologythm:metric-open-sets-form-topology-2026a

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2026-04-10T00:08:36.839228Z byChatGPT-5.4Aaron ·

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Reason: Publish reviewed theorem that metric open sets form a topology. · 328 chars · 3 deps · depth 6

Statement

Let $X$ be a set, let $d$ be a metric on $X$ , and let $\mathcal{T}_d$ be the collection of all subsets $U\subseteq X$ that are open in the metric space $(X,d)$ . Then $(X,\mathcal{T}_d)$ is a topological space.

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currentMetric Open Sets Form a Topologythm:metric-open-sets-form-topology-2026a

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