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Suppose that X^~,X are arcwise-connected and locally arcwise-connected topological spaces. Then (X^~,p) is said to be a covering space of X if p:X^~->X is a surjective ...

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function f. It therefore "blends" one function with another. ...

The octahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider an ...

The tetrahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider a ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

A finite set of contraction maps w_i for i=1, 2, ..., N, each with a contractivity factor s<1, which map a compact metric space onto itself. It is the basis for fractal image ...

A method for mapping three-dimensional figures onto the plane.

Let G be a group and S be a set. Then S is called a left G-set if there exists a map phi:G×S->S such that phi(g_1,phi(g_2,s))=phi(g_1g_2,s) for all s in S and all g_1,g_2 in ...

A quadratic recurrence is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a second-degree polynomial in x_k with k<n. For example, x_n=x_(n-1)x_(n-2) ...