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Let E be a set of expressions representing real, single-valued partially defined functions of one real variable. Let E^* be the set of functions represented by expressions in ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

In a lattice, any two elements a and b have a least upper bound. This least upper bound is often called the join of a and b, and is denoted by a v b. One can also speak of ...

Jung's theorem states that the generalized diameter D of a compact set X in R^n satisfies D>=Rsqrt((2(n+1))/n), where R is the circumradius of X (Danzer et al. 1963). This ...

The König-Egeváry theorem, sometimes simply called König's theorem, asserts that the matching number (i.e., size of a maximum independent edge set) is equal to the vertex ...

A representation of a Lie algebra g is a linear transformation psi:g->M(V), where M(V) is the set of all linear transformations of a vector space V. In particular, if V=R^n, ...

A link invariant is a function from the set of all links to any other set such that the function does not change as the link is changed (up to isotopy). In other words, a ...

Let L=(L, ^ , v ) be a lattice, and let f,g:L->L. Then the pair (f,g) is a local polarity if and only if for each finite set X subset= L, there is a finitely generated ...

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, ...