Glossary of mathematics

This is a glossary featuring terms used across different areas in mathematics, or terms that do not typically appear in more specialized glossaries. For the terms used only in some specific areas of mathematics, see glossaries in Category:Glossaries of mathematics.

B

binary: A binary relation is a set of ordered pairs; an element x is said to be related to another element y if and only if (x,y) are in the set.

C

canonical: 1. A canonical map is a map or morphism between objects that arises naturally from the definition or the construction of the objects being mapped against each other.; 2. A canonical form of an object is some standard or universal way to express the object.
correspondence: A correspondence from a set $A$ to a set $B$ is a subset of a Cartesian product $A\times B$ ; in other words, it is a binary relation but with the specification of the ambient sets $A,B$ used in the definition.

D

diagram: See mathematical diagram.

F

function: A function $f:A\to B$ is an ordered triple $(A,B,f)$ consisting of sets $A,B$ and a subset $f$ of the Cartesian product $A\times B$ subject to the condition $(a,b),(a,b')\in f$ implies $b=b'$ . In other words, it is a special kind of correspondence where given an element $a$ of $A$ , there is a unique element $b$ of $B$ that corresponds to it.

I

invariant: An invariant of an object or a space is a property or number of the object or a space that remains unchanged under some transformations.

M

map: A synonym for a function between sets or a morphism in a category. Depending on authors, the term "maps" or the term "functions" may be reserved for specific kinds of functions or morphisms (e.g., function as an analytic term and map as a general term).
mathematics: See mathematics.
multivalued: The term "multivalued function" is another term for a correspondence.

P

projection: A projection is, roughly, a map from some space or object to another that omits some information on the object or space. For example, $\mathbb {R} ^{2}\to \mathbb {R} ,(x,y)\mapsto x$ is a projection and its restriction to a graph of a function, say, is also a projection. The terms “idempotent operator” and “forgetful map” are also synonyms for a projection.

S

structure: A mathematical structure on an object is an additional set of objects or data attached to the object (e.g., relation, operation, metric, topology).

References

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Glossary of mathematics

B

C

D

F

I

M

P

S

See also

References