拟仿紧性与乘积空间

本文证明了在V=L假定下,所有正规局部紧拟仿紧空间是仿紧的．并证明了正则拟仿紧性在有限 对一闭映射下是逆保持的．还研究了狭义拟仿紧性的有限乘积和逆极限定理．     

几乎仿紧空间

主要证明了如下结果 :( 1 )如果 X =∏α∈ΛXα是 |Λ | -仿紧空间 ,则 X是几乎仿紧 (仿 - L indelof)空间当且仅当 F∈ [Λ ]<ω,∏α∈ FXα是几乎仿紧 (仿 - L indelof)空间 .( 2 )如果 X =∏i∈ωXi 是可数仿紧的 ,则下列三条等价 :X是几乎仿紧 (仿 - L indelof)的 : F∈ [ω]<ω,∏i∈ FXi是几乎仿紧 (仿 - L indelof)的 : n∈ω,∏i≤ nXi是几乎仿紧 (仿- Lindelof)的 .最后还给出了几乎仿紧 (仿 - L indelof)空间的一个刻划     

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。     

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.     

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．     

正规可数仿紧空间的逆极限

得到了如下结果:设X是逆系统{Xα,παβ,Λ}的逆极限,|Λ|=λ,假设每个映射πα∶X→Xα是开的且到上的,X是λ-仿紧,每个Xα是正规可数仿紧的,则X是正规可数仿紧的.进一步得到了关于遗传正规且遗传可数仿紧空间的类似结果.     

拟仿紧性与乘积空间

本文证明了在V=L假定下,所有正规局部紧拟仿紧空间是仿紧的.并证明了正则拟仿紧性在有限对一闭映射下是逆保持的.还研究了狭义拟仿紧性的有限乘积和逆极限定理.     

集合论在拟仿紧性中的应用

1977年,刘应明引进拟仿紧性并证明了下述集论拓扑学的结果：在假设$2^{\omega_1}>2^{\omega}$下每一个可分正规的拟仿紧空间是仿紧空间.我们进一步证明假设$2^{\omega_1}>2^{\omega}$等价于每一个可分正规的拟仿紧空间是仿紧空间,获得了拟仿紧性的一个独立性结果.     

关于Fréchet空间的仿紧性

引进了 σω(σκ)的定义 ,利用它刻划了 Fréchet空间 (κ′-空间 )的仿紧性 .主要结果是 :一个 Fréchet空间 (κ′-空间 )是仿紧的 它是正则的弱θ可加细空间且有性质σω(σκ)     

L—fuzzy拓扑空间中的层仿紧集

首先，在Ｌ－ｆｕｚｚｙ拓扑空间中引入了强α－局部有限族，并以此定义了比Ⅱ型强仿紧性更为广泛的层仿紧性，且讨论了层仿紧集的基本性质。其次，针对Ｌ－ｆｕｚｚｙ子集引入了层Ｈａｕｓｄｏｒｆｆ分离性，研究了它的基本特征。最后，讨论了弱诱导包含式正则空间中层仿紧集的特征。     

Strong paracompactness and w- -refinability of inverse limits

In this paper we construct inverse systems of which each space is strongly paracompact and each bonding map and each projection are open and onto maps, and the limit space is paracompact and not strongly paracompact and we investigate -refinability-like properties of limit spaces of inverse systems.

     

Continuous selections and -spaces

A characterization of paracompact -spaces via continuous selections avoiding -sets is given. The result is applied to prove a countable sum theorem for paracompact -spaces, and to obtain a new partial solution of a question raised by E. Michael.

     

LUSTERNIK-SCHNIRELMANN CATEGORY AND EMBEDDING FINITE COVERING MAPS, PRINCIPAL G-BUNDLES INTO BUNDLES

The author proves several embedding theorems for finite covering maps,principal G-bundies into bundles.The main results are 1. Let π：E→X be a finite covering map, and X a connected locally path-connected paracompact space. If cat X≤k, then the finite covering space π:E→X can be embedded into the trivial real k-plane bundle. 2. Let π：E→X be a principal G-bundle over a paracompact space. If there exists a linera action of Gon F(F=R or C)and cat X≤k ,then π：E→X can be embedded into ξ1 … ξn for any F-vector bundles ξi,i=1,…k.     

Characterizing maximal compact subgroups

We prove that for a compact subgroup H of a locally compact almost connected group G, the following properties are mutually equivalent: (1) H is a maximal compact subgroup of G, (2) the coset space G/H is \mathbbQ{\mathbb{Q}} -acyclic and \mathbbZ/2\mathbbZ{\mathbb{Z}/2\mathbb{Z}} -acyclic in Čech cohomology, (3) G/H is contractible, (4) G/H is homeomorphic to a Euclidean space, (5) G/H is an absolute extensor for paracompact spaces, (6) G/H is a G-equivariant absolute extensor for paracompact proper G-spaces having a paracompact orbit space.     

SOME RESULTS ABOUT COVERING PROPERTIES OF PRODUCTS

ＳＯＭＥ ＲＥＳＵＬＴＳ ＡＢＯＵＴ ＣＯＶＥＲＩＮＧ ＰＲＯＰＥＲＴＩＥＳ ＯＦ ＰＲＯＤＵＣＴＳ ￥ＪＩＡＮＧＪＩＧＵＡＮＧ;ＴＥＮＧＨＵＩＡｂｓｔｒａｃｔ：Ｔｈｅｆｏｌｌｏｗｉｎｇｒｅｓｕｌｔｓａｒｅｐｒｏｖｅｄ：１．ＬｅｔＸｂｅａｓｃｒｅｅｎ...     

Base-cover paracompactness

Call a topological space base-cover paracompact if has an open base such that every cover of contains a locally finite subcover. A subspace of the Sorgenfrey line is base-cover paracompact if and only if it is . The countable sequential fan is not base-cover paracompact. A paracompact space is locally compact if and only if its product with every compact space is base-cover paracompact.

     

Ladder systems on trees

We formulate the notion of uniformization of colorings of ladder systems on subsets of trees. We prove that Suslin trees have this property and also Aronszajn trees in the presence of Martin's Axiom. As an application we show that if a tree has this property, then every countable discrete family of subsets of the tree can be separated by a family of pairwise disjoint open sets. Such trees are then normal and hence countably paracompact. As a dual result for special Aronszajn trees we prove that the weak diamond, , implies that no special Aronszajn tree can be countably paracompact.

     

L-fuzzy拓扑空间中的几乎可数仿紧性

以可数仿紧性为背景,介绍几乎可数仿紧性的定义,并刻画其基本特征.深入研究L-fuzzy几乎可数仿紧性的性质,并证明几乎可敷仿紧性是"L-好的推广".     

无条件C的广义$\alpha \eta $}-单调性的判别标准

用$\alpha $和 $\eta $关于第一分量是仿射的且是斜对称的条件代替条件C, 得到如下结论: (1)如果一个函数的梯度是(严格)$\alpha \eta $-伪单调的,则该函数是(严格)伪$\alpha \eta $-不变凸的; (2)如果一个函数的梯度是拟$\alpha \eta $-单调的,则该函数是拟$\alpha \eta $-不变凸的.