On the product of relatively weakly almost Lindelöf subsets

The purpose of this note is to show that there exist two Tychonoff spaces X, Y, a subset A of X and a subset B of Y such that A is weakly almost Lindelöf in X and B is weakly almost Lindelöf in Y, but A × B is not weakly almost Lindelöf in X × Y.     

On ℒ-starcompact spaces

A space X is ?-starcompact if for every open cover of X, there exists a Lindelöf subset L of X such that St(L, ) = X. We clarify the relations between ?-starcompact spaces and other related spaces and investigate topological properties of ?-starcompact spaces. A question of Hiremath     

On Two Questions on Star-Lindeloef Spaces

In this paper, we give an example of a Hausdorff centered-Lindeloef space X such that St-l(X)=c^ , which negatively answers two questions rasied by Bonanzinga and Matveev.     

Lindelöf property and absolute embeddings

It is proved that a Tychonoff space is Lindelöf if and only if whenever a Tychonoff space contains two disjoint closed copies and of , then these copies can be separated in by open sets. We also show that a Tychonoff space is weakly -embedded (relatively normal) in every larger Tychonoff space if and only if is either almost compact or Lindelöf (normal almost compact or Lindelöf).

     

Spaces with large weak extent

In this paper, we show the following statements:

(1)

For any cardinal κ, there exists a pseudocompact centered-Lindelöf Tychonoff space X such that we(X)?κ.

(2)

Assuming ℵ₀²=ℵ₁², there exists a centered-Lindelöf normal space X such that we(X)?ω₁.

     

Fredholmness of pseudodifference operators in weighted Spaces

The aim of the paper is to present some results concerning pseudodifference operators on ?^N, which are a discrete analog of standard pseudodifferential operators on ?^N. We study the Fredholm property of pseudodifference operators acting in weighted l ^p spaces on ?^N and the Phragmen-Lindelöf principle for solutions of pseudodifference equations and give applications of these results to discrete Schrö dinger operators on ?^N.     

Some Topological Properties of Charming Spaces

In this paper, we mainly discuss the class of charming spaces. First, we show that there exists a charming space such that the Tychonoff product is not a charming space. Then we discuss some properties of charming spaces and give some characterizations of some class of charming spaces. Finally, we show that the Suslin number of an arbitrary charming rectifiable space is countable.     

$L$-Fuzzy拓扑空间中的可数紧性度和Lindel\"{o}f性质度

In this paper,the concept of countable compactness degree and the concept of Lindelf property degree are defined in L-fuzzy topological spaces by means of implication operator →.Many properties of them are discussed.     

关于置换空间P_B B_S

该文讨论了置换空间P_B B_S的序列收敛定理，逼近性质和度量投影T_Z的连续性，推广了［１］，［３］的相应结果．     

取值于序拓扑向量空间的映射与层空间

In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169(3): 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki's method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.     

A Brief Introduction to Fibrewise Topological Spaces Theory

Fibrewise topological spaces theory,presented in the recent 20 years,is a new branch of mathematics developed on the basis of General Topology,Algebra topology and Fibrewise spaces theory.It is associated with differential geometry,Lie groups and dynamical systems theory.From the perspective of Category theory,it is in the higher category of general topological space,so the discussion of new properties and characteristics of the variety of fibre topological space has more important significance.This paper introduces the process of the origin and development of Fibrewise topological spaces theory.Then,we study the main contents and important results in this branch.Finally,we review the research status of Fibrewise topological spaces theory and some important topics.     

局部β-凸空间中的第二分离性定理及其共轭锥上的有界性定理

第一部分给出局部β－凸空间中的第二分离性定理和Ｍｉｎｋｏｗｓｋｉ定理及Ｋｒｅｉｎ－Ｍｉｌｍａｎ定理等；第二部分得到其共轭锥上Ｕ Ｆ－有界与Ｕ Ｂ－有界等价的充要条件为原空间是次完备的．     

纤维拓扑空间理论简介

Fibrewise topological spaces theory,presented in the recent 20 years,is a new branch of mathematics developed on the basis of General Topology,Algebra topology and Fibrewise spaces theory.It is associated with differential geometry,Lie groups and dynamical systems theory.From the perspective of Category theory,it is in the higher category of general topological space,so the discussion of new properties and characteristics of the variety of fibre topological space has more important significance.This paper introduces the process of the origin and development of Fibrewise topological spaces theory.Then,we study the main contents and important results in this branch.Finally,we review the research status of Fibrewise topological spaces theory and some important topics.     

R(L$型诱导空间的分离性和良紧性

In this paper, we prove that （L^X,5） is T0,T1, T2, regular （T3）, normal （T4） and completely regular spaces if and only if （R（L）^X, ω（δ）） is T0, T1, T2, regular （T3）, normal （T4） and completely regular spaces, respectively, and （L^X,δ） is N-compact if and only if （R（L）^X, ω（δ）） is N-compact.     

Policy Iteration for Average Cost Markov Control Processes on Borel Spaces

This paper studies the policy iteration algorithm (PIA) for average cost Markov control processes on Borel spaces. Two classes of MCPs are considered. One of them allows some restricted-growth unbounded cost functions and compact control constraint sets; the other one requires strictly unbounded costs and the control constraint sets may be non-compact. For each of these classes, the PIA yields, under suitable assumptions, the optimal (minimum) cost, an optimal stationary control policy, and a solution to the average cost optimality equation.     

Semi-regular relative difference sets with large forbidden subgroups

Motivated by a connection between semi-regular relative difference sets and mutually unbiased bases, we study relative difference sets with parameters (m,n,m,m/n) in groups of non-prime-power orders. Let p be an odd prime. We prove that there does not exist a (2p,p,2p,2) relative difference set in any group of order 2p², and an abelian (4p,p,4p,4) relative difference set can only exist in the group . On the other hand, we construct a family of non-abelian relative difference sets with parameters (4q,q,4q,4), where q is an odd prime power greater than 9 and . When q=p is a prime, p>9, and , the (4p,p,4p,4) non-abelian relative difference sets constructed here are genuinely non-abelian in the sense that there does not exist an abelian relative difference set with the same parameters.     

Spaces embeddable as regular closed subsets into acc spaces and -spaces

It is well known that some classes of spaces such as absolutely countably compact (abbreviated acc) spaces and (a)-spaces are not hereditary with respect to closed, and even regular closed subspaces. In this paper, we investigate conditions for spaces being regular closed embeddable into spaces with certain covering properties, in particular we characterize spaces which can be embedded as regular closed subsets into acc spaces and (a)-spaces. Some examples are presented as applications of the criteria. Two problems raised by Matveev [Topology Appl. 80 (1997) 169–175] are answered.