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If X is a locally compact T2-space, then the set C_ degrees(X) of all continuous complex valued functions on X vanishing at infinity (i.e., for each epsilon>0, the set {x in ...

Given a Hilbert space H, the sigma-strong operator topology is the topology on the algebra L(H) of bounded operators from H to itself defined as follows: A sequence S_i of ...

A variety V of algebras is a strong variety provided that for each subvariety W of V, and each algebra A in V, if A is generated by its W- subalgebras, then A in W. In strong ...

The proposition that every proper ideal of a Boolean algebra can be extended to a maximal ideal. It is equivalent to the Boolean representation theorem, which can be proved ...

An Abelian category is a category for which the constructions and techniques of homological algebra are available. The basic examples of such categories are the category of ...

Let K be a field, and A a K-algebra. Elements y_1, ..., y_n are algebraically independent over K if the natural surjection K[Y_1,...,Y_n]->K[y_1,...,y_n] is an isomorphism. ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

The problem of maximizing a linear function over a convex polyhedron, also known as operations research or optimization theory. The general problem of convex optimization is ...

A proof of a formula on limits based on the epsilon-delta definition. An example is the following proof that every linear function f(x)=ax+b (a,b in R,a!=0) is continuous at ...

A system of linear differential equations (dy)/(dz)=A(z)y, (1) with A(z) an analytic n×n matrix, for which the matrix A(z) is analytic in C^_\{a_1,...,a_N} and has a pole of ...