拓扑分子格的S紧性和S次紧性

利用半开元等半拓扑概念在拓扑分子格中引入S紧性与S次紧性，给出了它们的刻画，推广了文[1]中的紧性与次紧性，证明了拓扑分子格的S紧性，S次紧性，STi分离性(i=-1，0，1，2)与STi^*分离性(i=0，1，2)为半拓扑性质。     

L-拓扑空间的相对Sβ-紧性

在L-拓扑空间中引入相对Sβ-紧性的概念,得到了它的一些性质,如它是L-好的推广,对闭子集遗传,被连续的广义Zadeh型函数所保持.此外,给出了相对Sβ-紧性的网式刻画.     

L-拓扑空间的相对S*-紧性

在L-拓扑空间中引入相对S*-紧性的概念,得到了它的一些性质,如它是L-好的推广,对子集遗传,被连续的广义Zadeh型函数所保持。此外,给出了相对S*-紧性的网式刻画。     

度量空间的紧覆盖s映射

本文引入了紧有限分解网的概念,给出度量空间的紧覆盖s象的内在刻画并由此导出度量空间s映射的系列结论,部分地回答了Michael-Nagami问题.     

遗传中紧空间与散射分解

本文证明了可数仿紧(中紧、亚紧)空间有类似Junnila的刻画，遗传中紧空间不具有类似Junnila的刻画，并给出了每个散射分解有紧有限的开膨胀的充要条件．     

p-仿紧空间

本文研究了p-仿紧空间和p-可数仿紧空间的相关问题.利用预开集和覆盖性质理论,得到了p-仿紧空间和p-可数仿紧空间的定义、等价刻画及αp-仿紧子集的性质,推广了一般拓扑学中仿紧空间的部分结果.     

局部可分度量空间的紧复盖紧映象

给出了局部可分度量空间紧复盖紧映象的刻画。     

遗传次亚紧空间

本文获得如下结果：（＊）Ｘ是遗传次亚紧空间当且仅当Ｘ的每个散射分解有个开的θ－膨胀序列．然后，利用这个结果推出了遗传次亚紧空间的两组等价刻画．最后，通过一个例子说明遗传仿紧空间不具有类似于（＊）的刻画．     

一类包含S—闭空间和紧空间的拓扑空间

本文定义了WS—闭空间的概念,它是S—闭空间和紧空间的推广.文中讨论了WS—闭空间的一些性质,推广了s—闭空间的一些结果.     

仿紧空间和S-闭空间的共同推广

定义了仿S紧空间的概念,它是仿紧空间和S－闭空间的共同推广,文中讨论了仿S紧密空间的一些性质,推广了仿紧空间和S－闭空间的部分结果。     

关于S-Lindelof 空间及其子空间

本文是在半开集理论中提出了S-Lindelf空间的概念.指出S-Lindelf空间是S-紧空间的一种推广,并对该空间及其子空间所具有的性质进行了一些有益的讨论.     

Merotopological Spaces

In this paper we introduce a new topological-type of structured set called merotopological space. The appropriate morphisms are defined and characterizations of the corresponding initial and final structures are given. The resulting category contains as fully embedded subcategories not only the category of topological spaces and continuous maps but also the category of merotopic spaces and uniformly continuous maps, and, a fortiori, the category of nearness spaces and the category of uniform spaces. A functorial completion is constructed for merotopological spaces using bunches. A problem that has remained long open in the setting of nearness spaces is to find an internal characterization of the epireflective hull of the topological spaces. We solve the analogue of this problem in the setting of merotopological spaces. Applications to the Wyler prime closed filter compactification and to Taimanov's extension theorem are given.     

Baire and Volterra spaces

In this paper we describe broad classes of spaces for which the Baire space property is equivalent to the assertion that any two dense -sets have dense intersection. We also provide examples of spaces where the equivalence does not hold. Finally, our techniques provide an easy proof of a new internal characterization of perfectly meager subspaces of and characterize metric spaces that are always of first category.

     

Stein domains in Banach algebraic geometry

In this article we give a homological characterization of the topology of Stein spaces over any valued base field. In particular, when working over the field of complex numbers, we obtain a characterization of the usual Euclidean (transcendental) topology of complex analytic spaces. For non-Archimedean base fields the topology we characterize coincides with the topology of the Berkovich analytic space associated to a non-Archimedean Stein algebra. Because the characterization we used is borrowed from a definition in derived geometry, this work should be read as a derived perspective on analytic geometry.     

Bloch space in the unit ball of

In this paper we obtain higher-dimensional versions of the Holland-Walsh characterization of the Bloch space and the Stroethoff characterization of the little Bloch space.

     

A characterization of Bloch space and Besov space

On the unit disk of the complex plane, a characterization for the membership of Bloch space and analytic Besov space is expressed extending known results.     

Characterization for Beurling-Björck space and Schwartz space

We give an elementary proof of the equivalence of the original definition of Schwartz and our characterization for the Schwartz space . The new proof is based on the Landau inequality concerning the estimates of derivatives. Applying the same method, as an application, we give a better symmetric characterization of the Beurling-Björck space of test functions for tempered ultradistributions with respect to Fourier transform without conditions on derivatives.

     

2维耗散准地转方程在齐次Morrey型Besov空间的适定性(英文)

本文讨论2维耗散准地转方程在齐次Morrey型Besov空间的初值问题.首先建立齐次Morrey型Besov空间的一个新特征,然后利用此特征和Kato方法,证明当初始值以齐次Morrey型Besov空间内的范数很小时,2维耗散准地转方程对时间的全局解的存在性和唯一性.