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A topological space X is pathwise-connected iff for every two points x,y in X, there is a continuous function f from [0,1] to X such that f(0)=x and f(1)=y. Roughly speaking, ...

A class of game in which players move alternately and each player is completely informed of previous moves. Finite, zero-sum, two-player games with perfect information ...

A characteristic of some systems making a transition to chaos. Doubling is followed by quadrupling, etc. An example of a map displaying period doubling is the logistic map.

A sequence {a_i} is said to be periodic with period p with if it satisfies a_i=a_(i+np) for n=1, 2, .... For example, {1,2,1,2,1,2,1,2,1,2,1,2,1,2,...} is a periodic sequence ...

A node in a graph for which the graph eccentricity equals the graph diameter (Harary 1994, p. 41).

The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector ...

The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspectrix or homology axis.

A singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

Let (xi_1,xi_2) be a locally Euclidean coordinate system. Then ds^2=dxi_1^2+dxi_2^2. (1) Now plug in dxi_1=(partialxi_1)/(partialx_1)dx_1+(partialxi_1)/(partialx_2)dx_2 (2) ...

Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.