Russian-English Dictionary of the Mathematical Sciences by A. J. Lohwater

By A. J. Lohwater

This is often at present the main entire and up to date source for examining and translating mathematical literature written in Russian. meant basically for these whose first language is English, this dictionary will turn out a great tool for researchers, editors, and translators operating with Russian mathematical literature.

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If L is a first-order language with a k-ary function or predicate symbol, for k ≥ 2, then there is no effective procedure that can determine whether or not an arbitrary sentence of L is logically valid. ) a < b for any a ∈ A, b ∈ B. The sets A and B form a Dedekind cut if A has a last element and B has no first element, or if A has no last element and B has a first element. ) is a Dedekind cut. If there exists a choice of A and B which is not a Dedekind cut, then X can be extended to an interval of R by including additional real numbers.

If the expression consists of only a finite number of fractions, the expression is called a finite continued fraction and is (obviously) a rational number. See also finite continued fraction. An infinite simple continued fraction is one of the form a0 + 1 a1 + 1 a2 + 1 a3 + 1 .. where each of the ai is an integer. See also convergence of a continued fraction. continuous function A function f from a topological space X to a topological space Y such that, for each open U ⊆ Y , the set f −1 (U ) is open in X.

2001 by CRC Press LLC dimensions of a rectangle The dimensions that fully describe a rectangle, namely length and width. Dimension Theorem of Affine Geometry Given affine space An , with nondisjoint subspaces Ar and As of dimension r and s, respectively, then r + s = dim(Ar ∪ As ) + dim(Ar ∩ As ). dimension theory The branch of topology devoted to the definition and study of the notion of dimension in various classes of topological spaces. dimension type Two topological spaces X and Y have the same dimension type if X is homeomorphic to a subspace of Y and Y is homeomorphic to a subspace of X.

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