Some geometric and topological properties of Banach spaces via ball coverings

By a ball-covering B of a Banach space X, we mean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that Gδ property of points in a Banach space X endowed with the ball topology is equivalent to the space X admitting the ball-covering property. Moreover, smoothness, uniform smoothness of X can be characterized by properties of ball-coverings of its finite dimensional subspaces.     

Modifications of uniform bases and classification of topological spaces

The notion of a uniform base, which was introduced by P. S. Alexandroff in 1960, turned out to be deeply connected with various properties of topological spaces. Modifications of this notion have led to new metrizability criteria and new directions in classification of topological spaces. A survey of the related results is given. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 34, General Topology, 2005.     

Two topological properties of topological linear spaces

A topological and a geometrical-topological property, previously known only for normed linear spaces, are established here for much more general classes of topological linear spaces. This research was conducted at the University of Washington in 1963 when the first author was visiting there. The work of both authors was supported in part by the National Science Foundation, U. S. A. (NSF-GP-378).     

On separation axioms in fuzzy topological spaces,fuzzy neighborhood spaces,and fuzzy uniform spaces

A certain number of separation axioms for fuzzy topological spaces are provided, all of which are good extensions of the topological (T₀), (T₁), or (T₂). All valid implications between the different axioms are studied and counterexamples are given for the nonvalid ones.     

软拓扑空间的分离性质

研究了软拓扑空间的相关性质.采用经典拓扑学的定义方法,定义了新的软点和软连续,证明了软拓扑空间及乘积拓扑空间有关的分离性质,通过例子说明了各种分离性质之间的关系,进一步推广了软拓扑空间.     

Selective covering properties of product spaces

We study the preservation of selective covering properties, including classic ones introduced by Menger, Hurewicz, Rothberger, Gerlits and Nagy, and others, under products with some major families of concentrated sets of reals.     

Some topological properties and fixed point results in cone metric spaces over Banach algebras

Positivity - This note is intended as an attempt at presenting some topological properties in cone metric spaces over Banach algebras. Moreover, the corresponding fixed point results are given. In...     

Expandable network and covering properties for uniform Eberlein compacta

In this paper we characterize the class of uniform Eberlein compact spaces through a network condition and also in terms of covering properties for the square of the space.