Linked from

The 36 pages that link to Cartesian product, each with the reason it gives.

• Coordinate systemRelated: Coordinate tuples use the same ordered structure, though their entries encode geometric positions.

• SetRelated: Cartesian products turn set elements into structured pairs.

• Axiom of choiceRelated: A choice function is exactly an element of this product when every factor is nonempty.

• Ordered pairRelated: It organizes ordered pairs into a set according to the allowed entries.

• SubsetRelated: Subset inclusion in either factor induces inclusion between the corresponding products.

• Indicator functionRelated: Indicators of product sets can be built from indicators of their factors.

• CardinalityRelated: Products reveal how cardinalities combine, including for infinite sets.

• Configuration spaceRelated: Ordered configurations begin in the product of one copy of the underlying space for each point.

• Empty setRelated: A Cartesian product with the empty set has no ordered pairs.

• Binary relationRelated: A relation from one set to another is a subset of their Cartesian product.

• Finite setRelated: Products of finitely many finite sets are finite, with sizes multiplied.

• Tensor productCompared with: The underlying pairs alone do not impose the bilinear relations that define a tensor product.

• Transitive relationRelated: A relation on a set is a subset of that set's Cartesian product.

• Binary operationRelated: The operation’s domain is the set paired with itself.

• Reflexive relationRelated: A relation on A is a subset of A × A, where reflexivity requires every diagonal pair.

• RelationRelated: Relational product pairs every tuple from one relation with every tuple from another.

• TorusRelated: Taking the product of two circles gives the torus.

• Choice functionRelated: Choice functions correspond to elements of products of nonempty sets.

• Product topologyNarrower topic: The product topology places a topology on this underlying set of tuples.

• Transition functionRelated: The transition function’s domain is commonly the product of states and input symbols.

• Axiom of pairingBroader topic: Its ordered pairs ultimately rely on set constructions enabled by pairing.

• Axiom of unionRelated: Its standard set-theoretic construction uses unions to assemble encoded ordered pairs.

• ElementRelated: Its elements combine membership in two sets into ordered pairs.

• Rule of productRelated: Each complete sequence of choices corresponds to one tuple in a Cartesian product.

• Tychonoff's theoremNarrower topic: The theorem concerns the topology placed on this underlying set.

• Set-builder notationRelated: Ordered-pair membership can be specified by conditions on each coordinate.

• Symmetric relationRelated: A relation's possible pairs are drawn from a Cartesian product.

• CombinationCompared with: It models ordered choices across positions, rather than an unordered selection.

• Quotient setCompared with: Products combine elements into tuples, whereas quotients identify elements into classes.

• Product (mathematics)Related: Its name and size connect multiplication with counting combinations.

• Tube lemmaNarrower topic: The lemma concerns open subsets of a product formed from a compact space and another space.

• Hales–Jewett theoremNarrower topic: A word space is a Cartesian power of its alphabet.

• Axiom of Empty SetRelated: An empty factor makes the product empty under the usual definition.

• Element of a setRelated: Membership in a product is determined by the pair's entries belonging to its factors.

• Family (mathematics)Related: A family of sets can be combined by choosing one element from every indexed set.

• Function of several real variablesRelated: A function's input tuples are drawn from products of real-number sets.