User christian clason - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T12:33:32Z http://mathoverflow.net/feeds/user/30516 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118442/reference-for-x-compact-c-bx-separable-x-metric-space/118461#118461 Answer by Christian Clason for reference for "X compact <=> C_b(X) separable" (X metric space) Christian Clason 2013-01-09T16:17:10Z 2013-01-09T20:05:28Z <p>The result does appear in Dunford/Schwartz, <em>Linear Operators Part I</em> (page 437), but is only stated as an exercise. </p> <p>Edit after @JosephVanName' comment: Conway's <em>Functional Analysis</em> has the result for completely regular spaces as Theorem 6.6 (page 140).</p> http://mathoverflow.net/questions/118829/difference-between-generalized-gradient-and-subgradient/118850#118850 Comment by Christian Clason Christian Clason 2013-01-14T10:22:07Z 2013-01-14T10:22:07Z I would also recommend Winfried Schirotzek's very nice book [Nonsmooth Analysis](<a href="http://www.springer.com/mathematics/analysis/book/978-3-540-71332-6?cm_mmc=Google-_-Book+Search-_-Springer-_-0&amp;otherVersion=978-3-540-71333-3" rel="nofollow">springer.com/mathematics/analysis/book/&hellip;</a>), which comprehensively covers many generalized differentials and their relations (in infinite dimensions). http://mathoverflow.net/questions/118515/derivative-indicator-function Comment by Christian Clason Christian Clason 2013-01-10T13:01:52Z 2013-01-10T13:01:52Z Could you add a bit more details? For example, it is important what you mean by indicator function -- the standard definition I know is extended-real-valued, and hence has no derivative in the sense of classical analysis. There are other derivative concepts that are applicable here, but it would help to know the context of this question. http://mathoverflow.net/questions/118442/reference-for-x-compact-c-bx-separable-x-metric-space/118461#118461 Comment by Christian Clason Christian Clason 2013-01-10T08:31:35Z 2013-01-10T08:31:35Z Well, a proof should not only convince the reader that a statement is true, but also explain why it is true. For the former, an appeal to authority (like a reference to an exercise in D&amp;S) is sufficient, but the latter requires pointing the reader to a full proof. That's why I did not think my first reply was a full answer. (Also, the references were suggested by others and I just checked them, so it seemed wrong to harvest the rep for them.)