Axiom of countability
In mathematics, an axiom of countability is a property of certain mathematical objects (usually in a category) that requires the existence of a countable set with certain properties, while without it such sets might not exist.
Thus, axioms of countability are not axioms in today's sense of the word; in this respect they are somewhat like the separation axioms.
Examples of mathematical objects for which axioms of countability hold include:
