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

A position in a game is unsafe for player A if the person who plays next (player B) can win. Every unsafe position can be made safe by at least one move.

A function f is said to have a upper bound C if f(x)<=C for all x in its domain. The least upper bound is called the supremum. A set is said to be bounded from above if it ...

The limit of an upper sum, when it exists, as the mesh size approaches 0.

For a given bounded function f(x) over a partition of a given interval, the upper sum is the sum of box areas M^*Deltax_k using the supremum M of the function f(x) in each ...

For every topological T1-space X, the following conditions are equivalent. 1. X is regular and second countable, 2. X is separable and metrizable. 3. X is homeomorphic to a ...

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 ...

The study of valuations which simplifies class field theory and the theory of function fields.

The quantity which a function f takes upon application to a given quantity.

A quantity which takes on the value zero is said to vanish identically, or sometimes simply to vanish. The term "vanish identically" is preferred when emphasis is needed that ...