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A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

The intersection of two sets A and B is the set of elements common to A and B. This is written A intersection B, and is pronounced "A intersection B" or "A cap B." The ...

A planar convex quadrilateral consisting of two adjacent sides of length a and the other two sides of length b. The rhombus is a special case of the kite, and the lozenge is ...

Lattice theory is the study of sets of objects known as lattices. It is an outgrowth of the study of Boolean algebras, and provides a framework for unifying the study of ...

Low-dimensional topology usually deals with objects that are two-, three-, or four-dimensional in nature. Properly speaking, low-dimensional topology should be part of ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

The word "median" has several different meanings in mathematics all related to the "middle" of mathematical objects. The statistical median is an order statistic that gives ...

A statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule (duality principle), or ...

In algebraic geometry classification problems, an algebraic variety (or other appropriate space in other parts of geometry) whose points correspond to the equivalence classes ...

In simple algebra, multiplication is the process of calculating the result when a number a is taken b times. The result of a multiplication is called the product of a and b, ...