Main Page | See live article | Alphabetical index 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: sigma-finite measure spacess first-countable and second-countable topological spaces Lindelöf spaces sigma-compact spaces separable spaces lattices of countable type This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.