Fuzzy拓扑线性空间的Fuzzy赋准范化

引进（ＱＬ）型Ｆｕｚｚｙ拓扑线笥空间的优基坯概念,在此基础上得到了分离的Ｆｕｚｚ６ｙ拓扑线性空间可Ｆｕｚｚｙ赋准范化的一个充分必要条件,进上步阐明了Ｆｕｚｚｙ准范线性空间与（ＱＬ）型Ｆｕｚｚｙ拓扑线笥空间的关系。     

拓扑空间可度量化的充要条件

本文研究了拓扑空间的可度量化的充要条件.利用可数开覆盖的性质和度量化的遗传性及定义,获得了拓扑空间可度量化的两个充要条件结果,推广了构造可度量化的拓扑空间和判断拓扑空间是度量空间的依据.     

赋序列范数的矢值Banach序列空间的光滑性与强光滑性

讨论了赋序列范数的矢值Banach序列空间ss(E)的光滑性与强光滑性,给出了它们的判据．     

模糊拓扑环的模糊复范化

引入环上的模糊复范数概念 ,得到模糊拓扑环可模糊复范化的充分必要条件 ,从而揭示出模糊拓扑环与普通拓扑环所不同的一个新特点 .     

赋序列范数的矢值Banach序列空间的强U-点和暴露点

刻划了赋序列范数的矢值Banach序列空间$ss(E)$的强U-点和暴露点,给出了它们的判据.     

赋序列范数的矢值序列空间ss(E)的强暴露性和暴露性

刻划了赋序列范数的矢值B anach序列空间ss(E)的强暴露性和暴露性,给出了它们的判据.     

强拟Si分离性及其拓扑性质

利用强拟开集引入了强拟分离性,给出了强拟Si-空间的等价刻画,最后研究了强拟分离的拓扑性质。     

关于可拓扑生成的LF拓扑空间的注记

给出可拓扑生成的LF拓扑空间的三条性质,它们分别推广了现有的相应结果。     

序列伪轨跟踪性与拓扑可迁

给出序列伪轨跟踪性的定义,得到拓扑可迁的一个充分条件,并证明,若f是同胚,则f具有序列伪轨跟踪性当且仅当其逆极限空间上的移位映射σf具有序列伪轨跟踪性。     

赋序列范数的矢值Banach序列空间ss(E)的凸性

本文对赋序列范数的矢值Banach序列空间ss(E)的一些凸性进行了讨论,得到的主要结果如下: 1.ss(E)是局部一致凸的当且仅当ss和E是局部一致凸的; 2.ss(E)是强凸的当且仅当ss和E是强凸的; 3.设ss和ss*具有AK性质,则ss(E)是非常凸的当且仅当ss和E是非常凸的.     

Invariant Metrizability and Projective Metrizability on Lie Groups and Homogeneous Spaces

In this paper, we study the invariant metrizability and projective metrizability problems for the special case of the geodesic spray associated to the canonical connection of a Lie group. We prove that such canonical spray is projectively Finsler metrizable if and only if it is Riemann metrizable. This result means that this structure is rigid in the sense that considering left invariant metrics, the potentially much larger class of projective Finsler metrizable canonical sprays, corresponding to Lie groups, coincides with the class of Riemann metrizable canonical sprays. Generalisation of these results for geodesic orbit spaces are given.

     

Metrizability and Coconnectedness

Solving the problem stated in Sichler and Trnková, Topol. Its Appl., 142: 159–179, 2004, we construct metrics μ, ν on a set P such that the spaces X=(P,μ) and Y=(P,ν) have the same monoid of all continuous selfmaps, the space Y is coconnected (in the sense that every continuous map Y×Y→Y depends on at most one coordinate) while X is not. Also, properties of the forgetful functors Metr → Unif → Top are investigated for the “simultaneous variant” of the above problem. Supported by the Grant Agency of Czech Republic under grant 201/06/0664 and by the project of Ministry of Education of Czech Republic MSM 0021620839.     

不分明化拓扑中强紧性

在不分明化拓扑空间中,从pre-开集出发引入了强紧性的概念,并且给出了它的一些性质.这些概念的结合有助于我们对不分明化拓扑的研究.     

Metrizability of Clifford topological semigroups

We prove that a countably compact Clifford topological semigroup S is metrizable if and only if the set E={e∈S:ee=e} of idempotents of S is a metrizable G _δ -set in S.     

Metrizability of spaces and weak base g-functions

In this paper, we give some metrization theorems and characterize some generalized metric spaces in terms of (weak base) g-functions. And we give quick proofs of two theorems in [Topology Appl. 91 (1999) 71].     

Metrizability of spaces of holomorphic functions

In this paper we prove that if U is an open subset of a metrizable locally convex space E of infinite dimension, the space H(U) of all holomorphic functions on U, endowed with the Nachbin-Coeuré topology τδ, is not metrizable. Our result can be applied to get that, for all usual topologies, H(U) is metrizable if and only if E has finite dimension.     

Metrizability of paratopological (semitopological) groups

We investigate some generalized metric space properties on paratopological (semitopological) groups and prove that a paratopological group that is quasi-metrizable by a left continuous, left-invariant quasi-metric is a topological group and give a negative answer to Ravsky?s question (Ravsky, 2001 [18, Question 3.1]). It is also shown that an uncountable paratopological group that is a closed image of a separable, locally compact metric space is a topological group. Finally, we discuss Hausdorff compactification of paratopological (semitopological) groups, give an affirmative answer to Lin and Shen?s question (Lin and Shen, 2011 [14, Question 6.9]) and improve an Arhangel?skii and Choban?s theorem. Some questions are posed.     

On the Metrizability of Fuzzy Neighborhood Spaces

A fuzzy neighborhood space is said to be pseudometrizable if, and only if, the associated fuzzy topology is induced by a probabilistic pseudometric under. By the aid of the concept of quasi-inverse functions it will be shown that a fuzzy neighborhood space is pseudometrizable if, and only if, every associated level-topology is pseudometrizable and a family of generating pseudometrics is monotone decreasing.     

Regular-Norm Balls can be Closed in the Strong Operator Topology

The main results obtained are:– A Dedekind complete Banach lattice Y has a Fatou norm if and only if, for any Banach lattice X, the regular-norm unit ball Ur = {T Lr(X,Y): ||T||r 1} is closed in the strong operator topology on the space of all regular operators, Lr(X,Y).– A Dedekind complete Banach lattice Y has a norm which is both Fatou and Levi if and only if, for any Banach lattice X, the regular-norm unit ball Ur is closed in the strong operator topology on the space of all bounded operators, L(X,Y).– A Banach lattice Y has a Fatou–Levi norm if and only if for every L-space X the space L(X,Y) is a Banach lattice under the operator norm.– A Banach lattice Y is isometrically order isomorphic to C(S) with the supremum norm, for some Stonean space S, if and only if, for every Banach lattice X, L(X,Y) is a Banach lattice under the operator norm.Several examples demonstrating that the hypotheses may not be removed, as well as some applications of the results obtained to the spaces of operators are also given. For instance:– If X = Lp() and Y = Lq(), where 1 < p,q < , then Lr(X,Y) is a first category subset of L(X,Y).     

The Density of the Hypercyclic Operators in the Strong Operator Topology

In this note we give a simple proof of the fact that the set of all hypercyclic operators on a separable Hilbert space is dense in the strong operator topology.