Timeline for When is a sequentially closed cone, closed?
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10 events
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| Feb 15, 2013 at 15:02 | comment | added | andy teich | But if you assume that the space is bornological, than this will surely impose some restriction on the seminorms which generate the topology, since not any locally convex space is bornological, but the topology of any locally convex space can be generated by some seminorms... | |
| Feb 15, 2013 at 7:26 | comment | added | Jochen Wengenroth | As for almost all locally convex properties, bornologicity does not reflect properties of single seminorms. The essential point is always the relation between them or how many of them you need. A trivial example: If only countably many seminorms describe the locally convex topology the space is (semi-) metrizable and hence bornological. | |
| Feb 14, 2013 at 14:57 | comment | added | andy teich | If you can write down the seminorms "explicitely", what condotions do you have to impose in order that thes space is bornologic? Maybe my question is not well defined... | |
| Feb 14, 2013 at 14:35 | comment | added | andy teich | ...sorry, I meanz bornologicity! | |
| Feb 14, 2013 at 13:02 | comment | added | Jochen Wengenroth | I do not understand this question. Barreledness is rather close to bornologicity, for instance, every (locally) complete bornological space is ultrabornological and hence barrelled. This means that barrelledness will not help you very much to conclude closed from sequentially closed. | |
| Feb 14, 2013 at 12:46 | comment | added | andy teich | So what does barreldness imply on the seminorms generating the topology of the space? | |
| Feb 14, 2013 at 8:36 | history | edited | Jochen Wengenroth | CC BY-SA 3.0 |
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| Feb 14, 2013 at 7:27 | history | edited | Jochen Wengenroth | CC BY-SA 3.0 |
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| Feb 12, 2013 at 16:30 | history | edited | Jochen Wengenroth | CC BY-SA 3.0 |
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| Feb 12, 2013 at 14:50 | history | answered | Jochen Wengenroth | CC BY-SA 3.0 |