TITLE: the example of ccc but not separable
QUESTION [7 upvotes]: 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.

REPLY [3 votes]: If you're interested in the relationship between the ccc and separability, you should read Stevo Todorcevic's survey "Chain condition methods in topology".
http://www.sciencedirect.com/science/article/pii/S0166864198001126
It's a very convincing pamphlet on the power of chain conditions, clarifying that relationship with such beautiful theorems as:
1) (Todorcevic) Let X be compact Hausdorff. If every subspace of $X^2$ has the ccc then $X$ is separable.
2) (Rosenthal) A compact Hausdorff space $X$ is ccc if and only if every weakly compact subspace of $C(X)$ is separable.
Also, there's a whole book dedicated to chain conditions. It's called "Chain conditions in topology", by Wistar Comfort and Stelios Negropontis (Cambridge Tracts in Mathematics #79, Cambridge University Press).