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．     

关于遗传可遮和遗传σ-亚紧可数乘积的注记

证明了在逆序列的情形下,可遮空间、强可遮空间在假设X是可数仿紧空间的条件下可被其极限空间保持,进一步证明了遗传可遮,遗传强可遮及遗传σ-亚紧性在无需对投射及极限空间X做任何假设的情况下即可被其逆极限空间保持.作为上述两个结果的应用,分别给出了两个相关的可数Tychonoff乘积定理.     

正规狭义拟仿紧的乘积性质

本文主要证明了如下一些结果(1)设     

正规狭义拟仿紧的乘积性质

本文主要证明了如下一些结果：（１）设Ｘ＝Ｌｉｍ并且每个投射πσ是开满映射,如果Ｘ是－仿紧的且每个 Ｘσ是正规狭义拟仿紧的,则 Ｘ是正规狭义拟仿紧的;如果 Ｘ是遗传－仿紧的且每个 Ｘσ是遗传正规狭义拟仿紧的．则 Ｘ是遗传正规狭义拟仿紧的． （２）如果 Ｘ＝是 －仿紧空间,则Ｘ是正规狭义拟仿紧的当且仅当 是正规狭义拟仿紧的．最后,还给出了诸多覆盖性质的可数乘积的一个等价性命题．     

σ-ortho紧的逆极限性质

主要证明了如下结果：设X=lim{Xσ，πρ^σ，∧}|∧||=λ，并且每个投射πσ：X→Xσ是开满映,若X是λ-仿紧的，并且每个Xσ是σ-ortho紧空间，则X是σ-ortho紧空间。进一步还可得到遗传σ-ortho紧性质的类似结果。     

亚紧性在选择理论中的一个刻划(英文)

本文利用集值映射的选择理论,对正则空间的亚紧性给予了一种刻划。本文同时推广了选择理论中的两个经典定理。     

相对拓扑的一些性质

讨论了相对超正则的充要条件及相对拓扑空间在映射下的一些性质，并定义了两类新的相对拓扑空间，给出了它们的一些性质．     

τ选择及其在BCO理论中的应用

本文利用τ弱仿紧空间的概念证明了一种τ选择的存在性。作为选择理论的应用，我们说明了具有可数序基的τ弱仿紧空间存在点τ的可数序基。     

FC-空间上的连续选择和邻近选择定理

给出了-些从仿紧拓扑空间到FC-空间的新的连续选择;也给出了-些从仿紧拓扑空间到局部FC-一致空间的新的邻近选择.这些结果改进且推广了-些近来的结论.     

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．     

Hereditary Upper Radical Properties and Dual Supplementing Radicals of Hereditary Radicals of Groups

One aim of this paper is to prove that for any hereditary radical property 𝒫, there exists a radical property 𝒫′ supplementing 𝒫. Certain hereditary upper radical properties of groups are constructed, and some of them are applied to formulate the necessary and sufficient condition for a hereditary radical 𝒫 and its supplementing radical 𝒫′ forming a dual pair.     

A New Characterization of Hereditary Algebras

In this short article, we prove that a finite dimensional algebra is hereditary if and only if there is no loop in its ordinary quiver and every τ-tilting module is tilting.     

On Right Hereditary Rings and Dedekind Domains

ＯｎＲｉｇｈｔＨｅｒｅｄｉｔａｒｙＲｉｎｇｓａｎｄＤｅｄｅｋｉｎｄＤｏｍａｉｎｓＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ，７３００７０）Ａｂｓ...     

Permutation Groups and Covering Properties

The paper considers the possible cardinalities of maximal cofinitarygroups and the cofinalities of permutation groups on the setof natural numbers. These two cardinals are compared with someother well-known cardinal invariants which are related to coveringproperties in several forcing models. An application of combinatorialgroup theory to a construction of a forcing partially orderedset is presented.     

Exceptional Pairs in Hereditary Categories

We study the category 𝒞(X, Y) generated by an exceptional pair (X, Y) in a hereditary category ?. If r = dim _k Hom(X, Y) ≥ 1 we show that there are exactly 3 possible types for 𝒞(X, Y), all derived equivalent to the category of finite dimensional modules mod(H _r ) over the r-Kronecker algebra H _r . In general 𝒞(X, Y) will not be equivalent to a module category. More specifically, if ? is the category of coherent sheaves over a weighted projective line 𝕏, then 𝒞(X, Y) is equivalent to the category of coherent sheaves on the projective line ?¹ or to mod(H _r ) and, if 𝕏 is wild, then every r ≥ 1 can occur in this way.     

实值函数与某些覆盖性质

In the paper [properties defined with semi-continuous functions and some related spaces',Houston J.Math.,2015,41(3):1097–1106] properties(U L)~(wl)_m,(U L)~K_m and(U L)_m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces,countably mesocompact spaces and countably metacompact spaces,respectively.In this paper,we continue with the study on the relationship between properties defined with real-valued functions and some covering properties.Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.     

遗传C~*-子代数与可补闭子模的关系定理

设 E是 Hilbert C~*-模,证明了E的每个闭子模均可补的充要条件是 K(E)的每个非零遗传C~*-子代数B,均有形式B=pK(E)p,其中p为L(E)中投影元。     

H—空间的覆盖性质及其应用

我们得到了Ｈ－空间闭（开）覆盖性质的几个定理，改进和推广了Ｓｐｅｒｎｅｒ，Ｋｌｅｅ，Ａｌｅｘａｎｄｒｏｆｆ－Ｐａｓｙｎｋｏｆｆ，Ｂｅｒｇｅ，Ｇｈｏｕｉｌａ－Ｈｏｕｒｉ，Ｄａｎｚｅｒ－Ｇｒｕｎｂａｕｍ－Ｋｌｅｅ，Ｋｙ Ｆａｎ，ｓｈｉｈ－Ｔａｎ，Ｈｏｒｖａｔｈ和Ｌａｓｓｏｎｄｅ等人的相应结果。作为应用，我们对ｌ．ｃ．－空间内的下半连续集值映象证明了一个几站不动点定理并且推广吉洪诺夫不动点定理到ｌ．ｃ．     

Hereditary atomicity in integral domains

If every subring of an integral domain is atomic, we say that the latter is hereditarily atomic. In this paper, we study hereditarily atomic domains. First, we characterize when certain direct limits of Dedekind domains are Dedekind domains in terms of atomic overrings. Then we use this characterization to determine the fields that are hereditarily atomic. On the other hand, we investigate hereditary atomicity in the context of rings of polynomials and rings of Laurent polynomials, characterizing the fields and rings whose rings of polynomials and rings of Laurent polynomials, respectively, are hereditarily atomic. As a result, we obtain two classes of hereditarily atomic domains that cannot be embedded into any hereditarily atomic field. By contrast, we show that rings of power series are never hereditarily atomic. Finally, we make some progress on the still open question of whether every subring of a hereditarily atomic domain satisfies ACCP.