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Given a reference triangle DeltaABC, the trilinear coordinates of a point P with respect to DeltaABC are an ordered triple of numbers, each of which is proportional to the ...

A theorem about (or providing an equivalent definition of) compact sets, originally due to Georg Cantor. Given a decreasing sequence of bounded nonempty closed sets C_1 ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

A problem related to the continuum hypothesis which was solved by Solovay (1970) using the inaccessible cardinals axiom. It has been proven by Shelah and Woodin (1990) that ...

A mathematical structure A is said to be closed under an operation + if, whenever a and b are both elements of A, then so is a+b. A mathematical object taken together with ...

A subset of a topological space which is compact with respect to the relative topology.

A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean ...

The maximal independence polynomial I_G(x) for the graph G may be defined as the polynomial I_G(x)=sum_(k=i(G))^(alpha(G))s_kx^k, where i(G) is the lower independence number, ...

A topological space X has a one-point compactification if and only if it is locally compact. To see a part of this, assume Y is compact, y in Y, X=Y\{y} and x in X. Let C be ...

An n-dimensional open ball of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Explicitly, the open ball with center x ...