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A d-dimensional framework is a pair (G,p) where G=(V,E) is a graph with vertex set V and edge set E and p:V->R^d is a map that assigns a point in R^d to each vertex of G. The ...

A set of vectors in Euclidean n-space is said to satisfy the Haar condition if every set of n vectors is linearly independent (Cheney 1999). Expressed otherwise, each ...

A relation R on a set S is antisymmetric provided that distinct elements are never both related to one another. In other words xRy and yRx together imply that x=y.

The dimension of a partially ordered set P=(X,<=) is the size of the smallest realizer of P. Equivalently, it is the smallest integer d such that P is isomorphic to a ...

A relation "<=" is called a preorder (or quasiorder) on a set S if it satisfies: 1. Reflexivity: a<=a for all a in S. 2. Transitivity: a<=b and b<=c implies a<=c. A preorder ...

The reflexive closure of a binary relation R on a set X is the minimal reflexive relation R^' on X that contains R. Thus aR^'a for every element a of X and aR^'b for distinct ...

The reflexive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same reflexive closure as R. Thus aR^'b for any elements a and b of X, ...

The maximum cardinal number of a collection of subsets of a t-element set T, none of which contains another, is the binomial coefficient (t; |_t/2_|), where |_x_| is the ...

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...

A topology is given by a collection of subsets of a topological space X. The smallest topology has two open sets, the empty set emptyset and X. The largest topology contains ...