Axioms of countability

In mathematics, an axiom of countability is a property of certain mathematical objects (usually in a category) that asserts the existence of a countable set with certain properties. Without such an axiom, such a set might not provably exist.

Important countability axioms for topological spaces include:

These axioms are related to each other in the following ways:

Other examples of mathematical objects obeying axioms of infinity include sigma-finite measure spaces, and lattices of countable type.

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