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What about $GL(n,\mathbb C)$? Is it open, dense in $M(n,\mathbb C)$?

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    Yes, and yes. This is a nice exercise.2011-01-25
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    Too bad the question is tagged topological vector spaces. I was going to say something about the Zariski topology (much as I loathe to think of it as a topology, at the moment).2011-01-25

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