The discrete countable chain condition
Margaret Reames Wiscamb · Proceedings of the American Mathematical Society · 1969
able. It is well known that a separable space satisfies the countable chain condition, and it is easy to find an example to show that the converse fails [6, p. 60]. That CCC implies DCCC is obvious from the definitions. An example of E. Michael [7] gives us a topological space that satisfies tl-he DCCC but not the CCC. This space is Lindelbf, hence satisfies the DCCC (Theorem 2.1), but has an uncountable subset with the discrete topology, hence does not satisfy the CCC.