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The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

A topological space X is locally compact if every point has a neighborhood which is itself contained in a compact set. Many familiar topological spaces are locally compact, ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

A quantified system of real algebraic equations and inequalities in variables {x_1,...,x_n} is an expression QS=Q_1(y_1)Q_2(y_2)...Q_m(y_m)S(x_1,...,x_n;y_1,...,y_m), where Q ...

The term domain has (at least) three different meanings in mathematics. The term domain is most commonly used to describe the set of values D for which a function (map, ...

If a is an element of a field F over the prime field P, then the set of all rational functions of a with coefficients in P is a field derived from P by adjunction of a.

The blossom algorithm (Edmonds 1965) finds a maximum independent edge set in a (possibly weighted) graph. While a maximum independent edge set can be found fairly easily for ...

A three-dimensional data set consisting of stacked two-dimensional data slices as a function of a third coordinate.

One of the Eilenberg-Steenrod axioms which states that, if X is a space with subspaces A and U such that the set closure of A is contained in the interior of U, then the ...