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Apr 30, 2012 at 4:57 comment added yaoliang I think I got the answer: It seems to be always true as long as the LCTVS is complete (which really is necessary for $Y^X$ is complete when $Y$ is so). It is in the book "Functional Analysis: Theory and Applications" by Robert E. Edwards, Ex. 6.17.
Apr 30, 2012 at 3:13 comment added Gerald Edgar Now, perhaps you should tell us what you found when you looked in a textbook on locally convex spaces...
Apr 30, 2012 at 2:27 history edited yaoliang CC BY-SA 3.0
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Apr 29, 2012 at 17:07 vote accept yaoliang
Apr 29, 2012 at 12:39 answer added Alberto Abbondandolo timeline score: 3
Apr 29, 2012 at 2:37 answer added Nik Weaver timeline score: 3
Apr 29, 2012 at 0:43 history asked yaoliang CC BY-SA 3.0