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I am surprised that no one mentioned the Baire category theorem.

I am not sure if you would have enough time to show many applications in 30 minutes but it is almost certain that they will end up using it at some point. HereHere are some applications discussed on MO.

I am surprised that no one mentioned the Baire category theorem.

I am not sure if you would have enough time to show many applications in 30 minutes but it is almost certain that they will end up using it at some point. Here are some applications discussed on MO.

I am surprised that no one mentioned the Baire category theorem.

I am not sure if you would have enough time to show many applications in 30 minutes but it is almost certain that they will end up using it at some point. Here are some applications discussed on MO.

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Burak
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I am surprised that no one mentioned the Baire category theorem.

I am not sure if you would have enough time to show many applications in 30 minutes but it is almost certain that they will end up using it at some point. Here are some applications discussed on MO.

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