I've found that function both open and closed but fail to be continuous. Now, I want to find an example of closed mapping that may not be continuous.

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    $\begingroup$ How about just $f(x) = \begin{cases} 0 & x < 0 \\ 1 & x \ge 0 \end{cases}$ $\endgroup$ – A.S Apr 4 '13 at 5:09
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    $\begingroup$ Superficially, the first sentence of your question seems to be enough to answer the second. Could you clarify please? $\endgroup$ – Erick Wong Apr 4 '13 at 5:28

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