Glossary of mathematics

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

See also: list of mathematical constants, list of mathematical symbols and Category:Mathematical terminology.

B

binary

A binary relation is a set of ordered pairs; two elements are said to be related if and only if they 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 that $(a,b),(a,b^{\prime })\in f$ implies $b=b^{\prime }$. 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 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.

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 forgets 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 synonyms for a projection.

S

structure

A mathematical structure on an object is an additional set of objects or data attached to the object.

See also

• Glossary of areas of mathematics

References

• Encyclopedia of Mathematics

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