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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 ...

The term "Cartesian" is used to refer to anything that derives from René Descartes' conception of geometry (1637), which is based on the representation of points in the plane ...

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 ...

An n-dimensional disk (sometimes spelled "disc") of radius r is the collection of points of distance <=r (closed disk) or <r (open disk) from a fixed point in Euclidean ...

The dominance relation on a set of points in Euclidean n-space is the intersection of the n coordinate-wise orderings. A point p dominates a point q provided that every ...

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 ...