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describe through mathematics how the central concepts of convergence and continuity transform from the usual Euclidean distance...

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Advance Math

describe through mathematics how the central concepts ofconvergence and continuity transform from the usual Euclideandistance on the real line, to the more abstract notion of distanceas given by a metric on a metric space, to finally a descriptionthat only refers to open sets. It should also describe how theconcept of topology emerges from metric spaces.

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