Axiom of countability
In mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties. Without such an axiom, such a set might not provably exist. Important examples. Important countability axioms for topological spaces include: Relationships with each other. These axioms are related to each other in the following ways: Related concepts. Other examples of mathematical objects obeying axioms of countability include sigma-finite measure spaces, and lattices of countable type.