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Continuous map

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Let f: X --> Y be a continuous map. Let A (SYMBOL) C.
Show that, if (FUNCTION1) is closed, then (FUNCTION2).

*(For complete problem, including proper citation of functions and symbols, please see attachment)

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Solution Preview

Please see the attachment.

First, I claim that .
Since , then . From the condition, we know is closed, this means that . But ...

Solution Summary

Let f: X --> Y be a continuous map. This is a proof if the function is closed.