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Let E be a compact connected subset of d-dimensional Euclidean space. Gross (1964) and Stadje (1981) proved that there is a unique real number a(E) such that for all x_1, ...

Measure theory is the study of measures. It generalizes the intuitive notions of length, area, and volume. The earliest and most important examples are Jordan measure and ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

A prime ideal is an ideal I such that if ab in I, then either a in I or b in I. For example, in the integers, the ideal a=<p> (i.e., the multiples of p) is prime whenever p ...

The topology on the Cartesian product X×Y of two topological spaces whose open sets are the unions of subsets A×B, where A and B are open subsets of X and Y, respectively. ...

The term "recursive function" is often used informally to describe any function that is defined with recursion. There are several formal counterparts to this informal ...

Suppose that f is an analytic function which is defined in the upper half-disk {|z|^2<1,I[z]>0}. Further suppose that f extends to a continuous function on the real axis, and ...

The 27 real or imaginary lines which lie on the general cubic surface and the 45 triple tangent planes to the surface. All are related to the 28 bitangents of the general ...

Surreal numbers are the most natural collection of numbers which includes both the real numbers and the infinite ordinal numbers of Georg Cantor. They were invented by John ...

A codimension one foliation F of a 3-manifold M is said to be taut if for every leaf lambda in the leaf space L of F, there is a circle gamma_lambda transverse to F (i.e., a ...