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An algebraic manifold is another name for a smooth algebraic variety. It can be covered by coordinate charts so that the transition functions are given by rational functions. ...

A Banach algebra A for which H^1(A,X^*)=Z^1(A,X^*)/B^1(A,X^*)=0 for all Banach A-bimodules X is called amenable (or Johnson amenable; Helemskii 1989, 1997). This notion was ...

A topological two-sphere in three-space whose exterior is not simply connected. The outer complement of Antoine's horned sphere is not simply connected. Furthermore, the ...

An axis is a line with respect to which a curve or figure is drawn, measured, rotated, etc. The most common axes encountered are commonly the mutually perpendicular Cartesian ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

A quartic surface which can be constructed as follows. Given a circle C and plane E perpendicular to the plane of C, move a second circle K of the same radius as C through ...

Cauchy conditions are initial conditions (time conditions) rather than boundary conditions (space conditions). An initial-value problem is often termed a Cauchy problem. ...

The term "closure" has various meanings in mathematics. The topological closure of a subset A of a topological space X is the smallest closed subset of X containing A. If R ...

Let P be a matrix of eigenvectors of a given square matrix A and D be a diagonal matrix with the corresponding eigenvalues on the diagonal. Then, as long as P is a square ...

The term endomorphism derives from the Greek adverb endon ("inside") and morphosis ("to form" or "to shape"). In algebra, an endomorphism of a group, module, ring, vector ...