Discontinuous non-linear mappings on locally convex direct limits
| dc.creator | Glockner, Helge | |
| dc.date | 2005-03-18 | |
| dc.date.accessioned | 2026-07-07T05:18:07Z | |
| dc.date.available | 2026-07-07T05:18:07Z | |
| dc.description | 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. | |
| dc.description | 11 pages, LaTeX; long preprint version including an appendix | |
| dc.identifier | https://arxiv.org/abs/math/0503387 | |
| dc.identifier | http://arxiv.org/abs/math/0503387 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74549 | |
| dc.subject | General Topology | |
| dc.subject | Functional Analysis | |
| dc.subject | 46F05, 46T20 (Primary) 46A13, 46M40, 22E65 (Secondary) | |
| dc.title | Discontinuous non-linear mappings on locally convex direct limits | |
| dc.type | text |