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The compact-open topology is a common topology used on function spaces. Suppose X and Y are topological spaces and C(X,Y) is the set of continuous maps from f:X->Y. The ...

Given a set S with a subset E, the complement (denoted E^' or E^_) of E with respect to S is defined as E^'={F:F in S,F not in E}. (1) Using set difference notation, the ...

The mapping of a grid of regularly ruled squares onto a cone with no overlap or misalignment. Cone nets are possible for vertex angles of 90 degrees, 180 degrees, and 270 ...

Given a triangle, draw a Cevian to one of the bases that divides it into two triangles having congruent incircles. The positions and sizes of these two circumcircles can then ...

"The" continuity axiom is an additional Axiom which must be added to those of Euclid's Elements in order to guarantee that two equal circles of radius r intersect each other ...

A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological ...

A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

The convexity coefficient chi(D) of a region D is the probability that the line segment connecting two random points in D is contained entirely within D. For a convex region, ...

Let f(t) and g(t) be arbitrary functions of time t with Fourier transforms. Take f(t) = F_nu^(-1)[F(nu)](t)=int_(-infty)^inftyF(nu)e^(2piinut)dnu (1) g(t) = ...