Timeline for Is the space of analytic sections of a vector bundle a Fréchet space?
Current License: CC BY-SA 4.0
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| Jun 4, 2022 at 6:48 | comment | added | terceira | The upshot is that you have a projective limit of a countable spectrum of inductive limits of countable spectra of Banach spaces. These underlying spaces and the linking mappings are nice enough but mixing projective and inductive limits can lead to headaches. | |
| Jun 4, 2022 at 6:42 | comment | added | terceira | Well, yes--the subject IS complicated. I am confident that it is NOT Baire (call this a conjecture since I have never sat down to write out a proof). The case of the real analytic functions on a compact interval (which is simpler) leads to a so-called Silva space (for which see Köthe's monograph) and these are never Baire, except in trivial situations. | |
| Jun 3, 2022 at 23:17 | comment | added | Eduardo Longa | @terceira is it Baire, for instance? Their paper seem very complicated.. | |
| Jun 3, 2022 at 3:00 | comment | added | terceira | The space of real analytic functions, say on the line, doesn't have a natural Fréchet structure--the appropriate lc topology thereon is notoriously more complicated. It might pay to check out the work of, for example, Martineau, Vogt, Dománski. | |
| Jun 3, 2022 at 0:05 | history | edited | Eduardo Longa | CC BY-SA 4.0 |
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| Jun 2, 2022 at 23:53 | history | edited | Eduardo Longa | CC BY-SA 4.0 |
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| Jun 2, 2022 at 22:46 | history | edited | Eduardo Longa | CC BY-SA 4.0 |
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| Jun 2, 2022 at 22:00 | history | edited | Eduardo Longa | CC BY-SA 4.0 |
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| Jun 2, 2022 at 21:52 | history | asked | Eduardo Longa | CC BY-SA 4.0 |