XA×B

XA×B is not a universally fixed symbol in mathematics. Its meaning depends on the surrounding context and the conventions of the field in which it appears. In many cases, XA×B is used as a shorthand for the Cartesian or direct product of several objects, with X, A, and B representing sets, spaces, or algebraic structures.

In set theory and topology, X, A, and B are typically sets or topological spaces. XA×B commonly denotes the Cartesian product X × A × B, which is the set of all ordered triples (x, a, b). The Cartesian product is associative, so this object is naturally isomorphic to (X × A) × B and to X × (A × B). If the factors carry additional structure, such as a topology or uniform structure, the product inherits the corresponding product structure. For topological spaces, the product topology is the standard choice on X × A × B.

In algebra, if X, A, and B are groups, rings, modules, or vector spaces, XA×B typically denotes their direct product X × A × B. The product is equipped with the componentwise operations, and if the factors are finite, its cardinality is the product of the cardinalities. Homomorphisms from the product correspond to triples of homomorphisms, one from each factor, when appropriate universal properties are considered.

Because XA×B is not a fixed notation, it is important to consult the defining context to determine whether it represents a Cartesian product, a direct product, or another construct. See also Cartesian product, direct product, and product topology for related concepts.