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Several flavors of the open mapping theorem state: 1. A continuous surjective linear mapping between Banach spaces is an open map. 2. A nonconstant analytic function on a ...

According to G. Pólya, the method of finding geometric objects by intersection. 1. For example, the centers of all circles tangent to a straight line s at a given point P lie ...

A point group is a group of symmetry operations which all leave at least one point unmoved. Although an isolated object may have an arbitrary Schönflies symbol, the ...

The Poisson-Charlier polynomials c_k(x;a) form a Sheffer sequence with g(t) = e^(a(e^t-1)) (1) f(t) = a(e^t-1), (2) giving the generating function ...

A presheaf C of categories consists of the following data: 1. For every local homeomorphism f:Y->X of topological spaces X, Y, a category C(f:Y->X); 2. For every diagram f ...

Let U=(U,<··>) be a T2 associative inner product space over the field C of complex numbers with completion H, and assume that U comes with an antilinear involution xi|->xi^* ...

For any constructible function f, there exists a function P_f such that for all functions t, the following two statements are equivalent: 1. There exists an algorithm A such ...

The sum c_q(m)=sum_(h^*(q))e^(2piihm/q), (1) where h runs through the residues relatively prime to q, which is important in the representation of numbers by the sums of ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...

The Robbins constant is the mean line segment length, i.e., the expected distance between two points chosen at random in cube line picking, namely Delta(3) = (1) = (2) = ...