I'm struggled with the problem. I need to proove that the convergence of the sequence of generalized functions in D' can't be defined by any metric (can't be metrizable). I've tried to use the fact that the sequence convergence in D is not metrizable. And then to prove by contradiction. But i failed and was told that it's the wrong way to do it. I'll appreciate any help or materials which can help me.
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Do you mean convergence when you write "conversion"? – md2perpe May 22 '20 at 19:57
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@md2perpe of course, sorry, edited – Ivan_Kontr May 22 '20 at 20:13
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Did you check this problem? It should be applicable to sequential convergence. – VoBo May 28 '20 at 14:58