Search Results for ""

Two topological spaces X and Y are homotopy equivalent if there exist continuous maps f:X->Y and g:Y->X, such that the composition f degreesg is homotopic to the identity ...

Given n matches (i.e., rigid unit line segments), find the number of topologically distinct planar arrangements which can be made (Gardner 1991). In this problem, two matches ...

If S is any nonempty partially ordered set in which every chain has an upper bound, then S has a maximal element. This statement is equivalent to the axiom of choice. Renteln ...

Given any straight line and a point not on it, there "exists one and only one straight line which passes" through that point and never intersects the first line, no matter ...

A Banach space is a complete vector space B with a norm ||·||. Two norms ||·||_((1)) and ||·||_((2)) are called equivalent if they give the same topology, which is equivalent ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

A set A of integers is said to be one-one reducible to a set B (A<<_1B) if there is a one-one recursive function f such that for every x, x in A=>f(x) in B (1) and f(x) in ...

A well-covered graph is a graph for which every minimal vertex cover has the same size, which is equivalent to every maximal independent vertex set being the same size. It is ...

An Andreini tessellation is a three-dimensional equivalent of a semiregular tessellation. There are 28 such tessellations.

Let P(G) denote the chromatic polynomial of a finite simple graph G. Then G is said to be chromatically unique if P(G)=P(H) implies that G and H are isomorphic graphs, in ...