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For any point P on the boundary of an ordinary ball, find a neighborhood of P in which the intersection with the ball's boundary cuts the neighborhood into two parts, each ...

Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...

There are at least two distinct (though related) notions of the term Hilbert algebra in functional analysis. In some literature, a linear manifold A of a (not necessarily ...

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^* ...

A version of set theory which is a formal system expressed in first-order predicate logic. Zermelo-Fraenkel set theory is based on the Zermelo-Fraenkel axioms. ...

The divergence theorem, more commonly known especially in older literature as Gauss's theorem (e.g., Arfken 1985) and also known as the Gauss-Ostrogradsky theorem, is a ...

A hyperfunction, discovered by Mikio Sato in 1958, is defined as a pair of holomorphic functions (f,g) which are separated by a boundary gamma. If gamma is taken to be a ...

A condition which must hold for a result to be true, but which does not guarantee it to be true. If a condition is both necessary and sufficient, then the result is said to ...

A module M is Noetherian if it obeys the ascending chain condition with respect to inclusion, i.e., if every set of increasing sequences of submodules eventually becomes ...

A chain complex is a sequence of maps ...-->^(partial_(i+1))C_i-->^(partial_i)C_(i-1)-->^(partial_(i-1))..., (1) where the spaces C_i may be Abelian groups or modules. The ...