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Algebraic Varieties
There is a close connection between di erential geometry and algebraic ge-ometry, and because di erential geometry is seen as a tool for applications (physics), the same is true for algebraic geometry. The topology in di erential geometry is the smallest topology making the analytic functions continuous. In algebraic geometry, we work with polynomials rather that power-series, so we use the smallest topology that makes rational functions continuous.
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