Editing Countable chain condition (section)

==Examples and properties in topology==
A [[topological space]] is said to satisfy the countable chain condition, or '''[[Mikhail Yakovlevich Suslin|Suslin's]] Condition''', if the partially ordered set of non-empty [[open subset]]s of ''X'' satisfies the countable chain condition, ''i.e.'' every [[pairwise disjoint]] collection of non-empty open subsets of ''X'' is countable. The name originates from  [[Suslin's problem|Suslin's Problem]].

* Every [[separable topological space]] has ccc. Furthermore, a [[Product topology|product space]] of arbitrary amount of separable spaces has ccc.
* A [[metric space]] has ccc if and only if it's separable.
* In general, a topological space with ccc need not be separable. For example, a [[Cantor cube]] <math>\{ 0, 1 \}^\kappa</math> with the [[product topology]] has ccc for any cardinal <math>\kappa</math>, though ''not'' separable for <math>\kappa > \mathfrak{c}</math>.
* Paracompact ccc spaces are [[Lindelöf space|Lindelöf]].
* An example of a topological space with ccc is the real line.