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- W1890958428 abstract "Consider the self-map F of the space of real-valued test functions on the line which takes a test function f to the test function sending a real number x to f(f(x))-f(0). We show that F is discontinuous, although its restriction to the space of functions supported in K is smooth (and thus continuous), for each compact subset K of the line. More generally, we construct mappings with analogous pathological properties on spaces of compactly supported smooth sections in vector bundles over non-compact bases. The results are useful in infinite-dimensional Lie theory, where they can be used to analyze the precise direct limit properties of test function groups and groups of compactly supported diffeomorphisms." @default.
- W1890958428 created "2016-06-24" @default.
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- W1890958428 date "2006-01-01" @default.
- W1890958428 modified "2023-10-18" @default.
- W1890958428 title "Discontinuous non-linear mappings on locally convex direct limits" @default.
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- W1890958428 doi "https://doi.org/10.5486/pmd.2006.2714" @default.
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