Mathematics

2006, No. 4

K.V. Lykov

A CRITERION OF SEPARABILITY OF THE EXTRAPOLATION SPACE

A new approach to definition of the extrapolation space was presented in [1]. The problem of the description of such spaces was stated there. The problems of separability and maximality of extrapolation spaces are studied in the present work. The necessary and sufficient conditions in terms of the parameter which defines the space are obtained.

Y.N. Kuzmin

PERFECT SPACES OF MEASURUBLE B-VALUED FUNCTIONS, II

In this paper we continue considering perfect spaces of measurable B-valued functions in weak topology (Vestnik of Samara State University, 2000, No. 2(16)). A criterion of sequential completeness and quasicompleteness are proved. The Radon–Nicodym property of B-space values is necessary and contained among sufficient conditions.

V.P. Tsvetov

ON A SPECIAL RESTRICTION OF REFLEXIVE AND SYMMETRIC RELATION TO AN EQUIVALENCE RELATION

This paper presents a technical algorithm for constructing an equivalence relation as a subset of reflexive and symmetric relation on a finite set. The term ”technical” means that an equivalence relation contains as many elements as possible.