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I'm not an expert, but I believe the space of Distributions (in any number of variables), (a.k.a. generalised functions, including the Dirac delta, its derivatives, etc.) as used in PDE theory, is a topological vector space, but non-metrisable; even though sequences are sufficient to do everything. However, the subspace of tempered (Schwartz) distributions, as used in Fourier Analysis, is metrisable; it is a Fréchet space(or Fr{\'e}chet if anyone knows how to produce those accents). |
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I'm not an expert, but I believe the space of Distributions (in any number of variables), (a.k.a. generalised functions, including the Dirac delta, its derivatives, etc.) as used in PDE theory, is a topological vector space, but non-metrisable; even though sequences are sufficient to do everything. However, the subspace of tempered (Schwartz) distributions, as used in Fourier Analysis, is metrisable; it is a Frechet Fréchet space (or Fr{\'e}chet if anyone knows how to produce those accents). |
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1 | [made Community Wiki] | ||
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I'm not an expert, but I believe the space of Distributions (in any number of variables), (a.k.a. generalised functions, including the Dirac delta, its derivatives, etc.) as used in PDE theory, is a topological vector space, but non-metrisable; even though sequences are sufficient to do everything. However, the subspace of tempered (Schwartz) distributions, as used in Fourier Analysis, is metrisable; it is a Frechet space (or Fr{\'e}chet if anyone knows how to produce those accents). |
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