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How to show that $L^2([0,1])$ is a set of first category in $L^1([0,1])$?

Thank you.

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    Welcome to Math.stackexchange. People can help you better if you tell us what you have tried to do, what your thoughts are, your guesswork, or any relevant information, really!2012-05-02
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    Also answered here: http://math.stackexchange.com/a/184042012-05-02
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    generic solution to all such problems: use the open mapping theorem. 2nd category implies onto.2012-05-02

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