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November 12th, 2016, 01:30 PM   #1
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Topological Space

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November 12th, 2016, 03:01 PM   #2
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Let U be an open set in Y containing F(x). The inverse image of U is open in X and contains x. By assumption this set contains all but a finite number of x_n. Therefore U will contain the images F(x_n) (all but a finite number). This means that F(x_n) converges to F(x).
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