The Axiom of Countable Choice and Pointfree Topology

The Axiom of Countable Choice is known to be equivalent, somewhat surprisingly, to certain conditions for frames involving the Lindelöf property, such as: all copowers of the discrete topology N on the set of natural numbers are Lindelöf. This paper presents an augmented version of the results known in this area, with simplified and more conceptual proofs, based on the systematic use of certain choice-free characterizations of the closed quotients of copowers of N and a particular representation of the coreflection associated with these, as well as their analogues for completely regular frames.