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A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological ...

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...

If F is a sigma-algebra and A is a subset of X, then A is called measurable if A is a member of F. X need not have, a priori, a topological structure. Even if it does, there ...

A Lie algebra g is solvable when its Lie algebra commutator series, or derived series, g^k vanishes for some k. Any nilpotent Lie algebra is solvable. The basic example is ...

Let K be a class of topological spaces that is closed under homeomorphism, and let X be a topological space. If X in K and for every Y in K such that X subset= Y, X is a ...

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

A space which is isomorphic to a Borel subset B of a Polish space equipped with its sigma-algebra of Borel sets.

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 ...