On resolutions of generalized metric spaces

We study the relation between generalized metric spaces and their resolutions. Here, we consider the class of spaces with G_δ-diagonals, M₃-,M₁-spaces, M₃–μ-spaces and developable spaces.     

Normal covers of infinite products and normality of Σ-products

We give some characterizations for normal covers of infinite products of generalized metric spaces such as M-spaces, Σ-spaces and β-spaces. We prove them simultaneously in terms of β-spaces and perfect maps. Next, we give affirmative answers to two questions concerning the normality of Σ-products, which were raised by the author and Yamazaki, respectively. These results are stated in terms of Σ-products of β-spaces.     

关于《M1-空间的和定理》一文的注记

《数学研究与评论》1988年第一期研究通讯栏目上刊登了论文《M_1-空间的和定理》。我们这篇简短的注记在于说明: (1)上述论文所引进的“强遗传闭包保持集族”的概念等价于“遗传闭包保持集族”的概念。 (2)上述论文中的定理3的结论是不正确的。 关于(1)若正则拓扑空间X的子集族B是X的遗传闭包保持集族,那么由B的元的闭包所组成的集族亦是X的遗传闭包保持集族。     

On M-structures

We introduce the notion of M-structures and consider the class $\text{M}$ of stratifiable spaces with M-structures. Especially we study the relation between the class $\text{M}$ and that of M₁-spaces.     

M-harmonic Besovp-spaces and Hankel operators in the Bergman space on the ball in ℂ n

In this paper, we characterize the Hardy class ofM-harmonic functions on the unit ballB in ℂ ⁿ in terms of the Berezin transform. We define and study the Besovp-spaces ofM-harmonic functions. For anM-harmonic symbolf, we give various criteria for the Hankel operatorsH _f andH _f to be bounded, compact or in the Schatten-von-Neumann classS _p . These criteria establish a close relationship among Besovp-spaces, Berezin transform, the invariant Laplacian, and Hankel operators on the unit ballB.     

Geometrical properties of subclasses of complexL 1-preduals

We introduce the concept of a center of a set of complex functions. The concept is used to extend to complex spaces the max + min characterization of realG-spaces given by Lindenstrauss and Wulbert, to give geometrical and algebraic characterizations of complexC _o-spaces and to characterizeM-ideals.     

A representation theorem for maxitive measures

A maxitive measure is a nonnegative function η on a σ-algebra Σ and such that η(U_j A_j ) = sup_j η(A_j) for all countable disjoint families of sets (A_j) in Σ. A representation theorem for such measures is established, and next applied to represent Köthe function M-spaces as L_∞-spaces.     

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.     

Model-theoretic aspects of the Gurarij operator system

We establish some of the basic model theoretic facts about the Gurarij operator system GS recently constructed by the second-named author. In particular, we show: (1) GS is the unique separable 1-exact existentially closed operator system; (2) GS is the unique separable nuclear model of its theory; (3) every embedding of GS into its ultrapower is elementary; (4) GS is the prime model of its theory; and (5) GS does not have quantifier-elimination, whence the theory of operator systems does not have a model companion. We also show that, for any q ∈ ?, the theories of M_q-spaces and M_q-systems do have a model companion, namely the Fra¨?ssé limit of the class of finite-dimensional M_q-spaces and M_q-systems respectively; moreover, we show that the model companion is separably categorical. We conclude the paper by showing that no C* algebra can be existentially closed as an operator system.