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Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

"The" continuity axiom is an additional Axiom which must be added to those of Euclid's Elements in order to guarantee that two equal circles of radius r intersect each other ...

Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...

A series suma(n)e^(-lambda(n)z), where a(n) and z are complex and {lambda(n)} is a monotonic increasing sequence of real numbers. The numbers lambda(n) are called the ...

The 21 assumptions which underlie the geometry published in Hilbert's classic text Grundlagen der Geometrie. The eight incidence axioms concern collinearity and intersection ...

There are two possible definitions: 1. Possessing similarity of form, 2. Continuous, one-to-one, in surjection, and having a continuous inverse. The most common meaning is ...

A homeomorphism, also called a continuous transformation, is an equivalence relation and one-to-one correspondence between points in two geometric figures or topological ...

A hyperfunction, discovered by Mikio Sato in 1958, is defined as a pair of holomorphic functions (f,g) which are separated by a boundary gamma. If gamma is taken to be a ...

An infinitesimal transformation of a vector r is given by r^'=(I+e)r, (1) where the matrix e is infinitesimal and I is the identity matrix. (Note that the infinitesimal ...

Let I be a set, and let U be an ultrafilter on I, let phi be a formula of a given language L, and let {A_i:i in I} be any collection of structures which is indexed by the set ...