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Mathematics · L5 · Topology: Structure Hierarchy

How a metric space induces a topology, and the separation/connectedness/compactness properties a topological space may or may not have.

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Metric space (X, d)Topological space (X, τ)open balls generate τBasis Bgenerates τ via unionsContinuityf⁻¹(open) is openPropertiesHausdorff(unique limits)Connected(no clopen split)Compact(finite subcover)Continuous bijectionwith continuous inverse= Homeomorphism

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