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Let S be a nonempty set, then an ultrafilter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F. 2. If A,B in F, then A ...

A uniquely complemented lattice is a complemented lattice (L, ^ , v ,0,1,^') that satisfies ( forall x in L)( forall y in L)[(x ^ y=0) ^ (x v y=1)]=>y=x^'. The class of ...

The unlink, also called the trivial link, of n components consist of n disjoint circles in a plane (Rolfsen 1976, p. 65).

Let (K,|·|) be a valuated field. The valuation group G is defined to be the set G={|x|:x in K,x!=0}, with the group operation being multiplication. It is a subgroup of the ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

The number of graph edges meeting at a given node in a graph is called the order of that graph vertex.

Vorobiev's theorem states that if F_l^2|F_k, then F_l|k, where F_n is a Fibonacci number and a|b means a divides b. The theorem was discovered by Vorobiev in 1942, but not ...

Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.

A function, continuous in a finite closed interval, can be approximated with a preassigned accuracy by polynomials. A function of a real variable which is continuous and has ...

The negative integers ..., -3, -2, -1.