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A linear approximation to a function f(x) at a point x_0 can be computed by taking the first term in the Taylor series f(x_0+Deltax)=f(x_0)+f^'(x_0)Deltax+....

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the local discrepancy is defined as D(J,P)=|(number of x_n in J)/N-Vol(J)|, Vol(J) is the ...

A locally finite space is one for which every point of a given space has a neighborhood that meets only finitely many elements of any cover.

The four planes determined by the four altitudes of a tetrahedron and the orthocenters of the corresponding faces pass through the Monge point of the tetrahedron.

Given a marked point process Phi of the form Phi=(T,Y)=((T_n)_(n>=1),(Y_n)_(n>=1)), the space Y=(Y_n)_(n>=1) is said to be the mark space of Phi.

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

A function for which several distinct functional values correspond (as a result of different continuations) to one and the same point (Knopp 1996, p. 94).

A base for a neighborhood system of a point x is a collection N of open sets such that x belongs to every member of N, and any open set containing x also contains a member of ...

In a topological space X, an open neighborhood of a point x is an open set containing x. A set containing an open neighborhood is simply called a neighborhood.

The y- (vertical) coordinate of a point in a two dimensional coordinate system. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the ...