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A weak pseudo-Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is symmetric and for which, at each m in M, g_m(v_m,w_m)=0 for all w_m in T_mM implies ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

A prize of 100000 German marks offered for the first valid proof of Fermat's last theorem (Ball and Coxeter 1987, p. 72; Barner 1997; Hoffman 1998, pp. 193-194 and 199). The ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

The version of set theory obtained if Axiom 6 of Zermelo-Fraenkel set theory is replaced by 6'. Selection axiom (or "axiom of subsets"): for any set-theoretic formula A(u), ...

Given two additive groups (or rings, or modules, or vector spaces) A and B, the map f:A-->B such that f(a)=0 for all a in A is called the zero map. It is a homomorphism in ...

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 ...

Trigonometry

The first de Villiers point is the perspector of the reference triangle and its BCI triangle, which is Kimberling center X_(1127) and has triangle center function ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...