In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in...

graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and two...

can often define a direct product of objects already known, giving a new one. This induces a structure on the Cartesian product of the underlying sets from...

mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This...

product Interior product Outer product Tensor product In set theory, a Cartesian product is a mathematical operation which returns a set (or product set)...

geometry Cartesian morphism, formalisation of pull-back operation in category theory Cartesian oval, a curve Cartesian product, a direct product of two...

such as the Cartesian product of sets, the direct product of groups or rings, and the product of topological spaces. Essentially, the product of a family...

on an n-ary Cartesian product of partially ordered sets; this order is a total order if and only if all factors of the Cartesian product are totally ordered...

categorical product is the usual Cartesian product, and the terminal object is a singleton set. In the category of groups the categorical product is the Cartesian...

group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics. In the context of...

of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two...

Cartesian product.[citation needed] Cartesian product – a product of two sets Geometric algebra: Rotating systems Multiple cross products – products involving...

product Cartesian product of sets Direct product of groups Semidirect product Product of group subsets Wreath product Free product Zappa–Szép product (or...

In geometry, a Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely...

calculus Scatter matrix Cartesian product Cross product Exterior product Hadamard product (matrices) Bra–ket notation for outer product Complex conjugate Conjugate...

the product order (also called the coordinatewise order or componentwise order) is a partial ordering ≤ {\displaystyle \leq } on the Cartesian product A...

W {\displaystyle V\otimes W} is the set of the functions from the Cartesian product B V × B W {\displaystyle B_{V}\times B_{W}} to F that have a finite...

is defined as any topological space that is homeomorphic to the Cartesian product of three circles, T 3 = S 1 × S 1 × S 1 . {\displaystyle \mathbb {T}...

In topology, the cartesian product of topological spaces can be given several different topologies. One of the more natural choices is the box topology...

product in seven dimensions A product in a Künneth theorem A crossed product in von Neumann algebras A Cartesian product in set theory Cross-multiplication...

In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with...

the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely the projection product) of Euclidean...

subgroup. an outer semidirect product is a way to construct a new group from two given groups by using the Cartesian product as a set and a particular multiplication...

In mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings...

the product itself as rooted, at (g1, h1). The rooted product is a subgraph of the cartesian product of the same two graphs. The rooted product is especially...

Box product may refer to: The scalar triple product of three vectors A cartesian product of topological spaces equipped with the box topology The cartesian...

x2 if and only if f(x1) ≤ f(x2). The lexicographical order on the Cartesian product of a family of totally ordered sets, indexed by a well ordered set...

graph theory, the tensor product G × H of graphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and vertices...

matrices of two graphs is the adjacency matrix of the Cartesian product graph. The Kronecker product can be used to get a convenient representation for some...

algebra, denotes the cross product. 3.  In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory...