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A subset B of a vector space E is said to be balanced if lambdaB subset= B whenever lambda is a scalar satisfying |lambda|<=1. Here, the notation lambdaB denotes the set ...

The Banach density of a set A of integers is defined as lim_(d->infty)max_(n)(|{A intersection [n+1,...,n+d]}|)/d, if the limit exists. If the lim is replaced with lim sup or ...

Let f be a contraction mapping from a closed subset F of a Banach space E into F. Then there exists a unique z in F such that f(z)=z.

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ...

When working over a collection of fields, the base field is the intersection of the fields in the collection, i.e., the field contained in all other fields.

A basepoint is the beginning and ending point of a loop. The fundamental group of a topological space is always with respect to a particular choice of basepoint.

The word basis can arise in several different contexts. Speaking in general terms, an object is "generated" by a basis in whatever manner is appropriate. For example, a ...

One baud is defined as the state of a signal in a communication channel changing once per second.

Baud rate is a measure of the number of times per second a signal in a communications channel changes state. The state is usually voltage level, frequency, or phase angle.

The kernel of a symmetric bilinear form Q:V×V-->R is the set Ker(Q)={v in V|Q(v,w)=0 for all w in V}.