I am interested in the relation between the property of countable chain condition (ccc) and the property of separable. Could someone recommend some papers or books about this to me? thanks in advance.



the example of ccc but not separable
Nathan's answer seems to indicate that there are some strange spaces that are ccc but not separable. But in fact, such spaces are rather common:


All products of separable Hausdorff spaces are ccc, but if the spaces have at least two different points, then products with more than $2^{\aleph\_0}$ factors are not separable anymore. You can find this is basic books on topology, such as Engelking's book.


Also, in set-theoretic forcing, partial orders with the ccc are very common.
If you take the completion of a ccc po, you get a ccc Boolean algebra whose Stone space is ccc. Separability of the Stone space translates into $\sigma$-centeredness of p.o.s.
And there are a lot of partial orders used in forcing that are ccc but not $\sigma$-centered. 


