mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable...

Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union...

mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties...

In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets. The inductive definition above is well-founded...

  A set of formulas in the Lévy hierarchy ρ The rank of a set σ countable, as in σ-compact, σ-complete and so on Σ 1.  A sum of cardinals 2.  A set of...

null set is a Lebesgue measurable set of real numbers that has measure zero. This can be characterized as a set that can be covered by a countable union...

In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence...

countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty sets...

mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related...

In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in French with F for fermé (French: closed) and...