I know that determinant as a map from set $n×n$ matrices to $\Bbb{R}$ is an open map but I wonder whether it is closed map too?I don't know how to prove or disprove but intuitively it seems to me that it is not closed.Any help is appreciable
Thanks.
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1See the answer @Daniel Robert-Nicoud gave to this question – Peter Melech Apr 04 '21 at 12:53
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@Peter Melech very nice answer...thanks for your help – Ibrahim Islam Apr 04 '21 at 12:57
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1@lbs You're welcome! – Peter Melech Apr 04 '21 at 12:58
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@peter what about trace of matrix? Is it closed,.....again trace is open but can't think whether it a closed map! – Ibrahim Islam Apr 04 '21 at 13:01
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1It is not closed. Consider $A={\operatorname{diag}(n+n^{-1},-n)\mid n=1,2,3,\dots}$ and trace maps $A$ to ${n^{-1}\mid n=1,2,3,\dots}$. – user10354138 Apr 04 '21 at 13:13
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@Dietrich yes that helps as suggested by peter – Ibrahim Islam Apr 04 '21 at 13:21