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".     

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.     

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.     

L—Fuzzy拓扑空间中的可数F紧性与几乎可数F紧性

本文在Ｌ－ｕｚｚｙ拓扑空间中引入可数Ｆ紧性与几乎可数Ｆ紧性的概念，并讨论了它们的性质及其相互关系。     

一类仿紧连通空间的几乎开映像

讨论了包含仿紧连通空间的一些广义度量空间类的映射性质,证明了T1的连通第一可数空间是连通Lasnev空间的几乎开映像,部分回答了1998年Tkachuk关于连通空间逆像的一个问题;证明了T1的连通的具有点Gδ性质的空间是连通M1空间的几乎开映像,其中建立了M1空间的一个映射定理,回答了1976年Nyikos提出的一个问题.     

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．     

关于完全仿紧空间的一些刻画

本文在Ｔ１正则的条件下得到了完全仿紧空间的一些等价刻画,并利用所得到的刻画证明了这类空间的一个可数乘积定理。     

Extension dimension for paracompact spaces

We prove existence of extension dimension for paracompact spaces. Here is the main result of the paper:

Theorem. Suppose X is a paracompact space. There is a CW complex K such that

(a) K is an absolute extensor of X up to homotopy,

(b) If a CW complex L is an absolute extensor of X up to homotopy, then L is an absolute extensor of Y up to homotopy of any paracompact space Y such that K is an absolute extensor of Y up to homotopy.

The proof is based on the following simple result (see Theorem 1.2).

Theorem. Let X be a paracompact space. Suppose a space Y is the union of a family {Y_s}_sS of its subspaces with the following properties:

(a) Each Y_s is an absolute extensor of X,

(b) For any two elements s and t of S there is uS such that Y_sY_tY_u.

If f :A→Y is a map from a closed subset A to Y such that A=_sSInt_A(f⁻¹(Y_s)), then f extends over X.

That result implies a few well-known theorems of classical theory of retracts which makes it of interest in its own.     

Uniformly superparacompact,completely paracompact,and strongly paracompact uniform spaces

In this paper, we introduce and study uniform analogs of complete paracompactness, strong paracompactness, and superparacompactness. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 34, General Topology, 2005.     

A note on the class of paracompact spaces whose product with every paracompact space is paracompact

We prove that if X is a paracompact space which has a neighborhood assignment x→Hx such that for each y∈X the closure of the set is compact then the products T×X, for every paracompact space T, and Xω are paracompact. The first result answers a problem of H. Junnila.     

When countably paracompact,locally compact,screenable spaces are paracompact

Z. Balogh has shown that all normal, locally compact, screenable spaces are paracompact; it is known that the countably paracompact analogue of this theorem holds assuming V = L; in this paper we show that it also holds assuming Axiom R + MA_ω1, both of which follow from Martin's Maximum or PFA⁺(1), strengthenings of the Proper Forcing Axiom.     

关于完全强仿紧空间的刻画

在正则T1的条件下得到了完全强仿紧空间的一些等价刻画,并且利用获得的刻画证明了这类空间的一个可数乘积定理.     

Nearly uniformly noncreasy Banach spaces

We introduce and study the class of nearly uniformly noncreasy Banach spaces. It is proved that they have the weak fixed point property. A stability result for this property is obtained.     

Locally compact,countably paracompact spaces in the constructible universe

It is proven that under V = L, every locally compact, countably paracompact space is collectionwise normal with respect to compact sets. From this it can be shown that under V = L, submetacompact implies paracompact in the class of locally compact, countably paracompact spaces.     

Monotonically countably paracompact, collectionwise Hausdorff spaces and measurable cardinals

We show that, if an MCP (monotonically countably paracompact) space fails to be collectionwise Hausdorff, then there is a measurable cardinal and that, if there are two measurable cardinals, then there is an MCP space that fails to be collectionwise Hausdorff.