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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 ...

Given a vector space V, its projectivization P(V), sometimes written P(V-0), is the set of equivalence classes x∼lambdax for any lambda!=0 in V-0. For example, complex ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

A characterization of normal spaces with respect to the definition given by Kelley (1955, p. 112) or Willard (1970, p. 99). It states that the topological space X is normal ...

Over a small neighborhood U of a manifold, a vector bundle is spanned by the local sections defined on U. For example, in a coordinate chart U with coordinates (x_1,...,x_n), ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

R^- denotes the real negative numbers.

R^+ denotes the real positive numbers.

An algebraic variety over a field K that becomes isomorphic to a projective space.