关于单调亚紧空间

In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fó-subspaces. For a generalized ordered (GO)-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X* is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.     

Monotone normality and paracompactness

In this paper it is proved that a topological space is necessarily paracompact if it is monotonically normal and any one of the following: screenable, paralindelöf, has a G_δ-diagonal or a quasi-G_δ-diagonal or has a σ-locally-countable base.     

Erratum to “Normality and countable paracompactness of hyperspaces of ordinals” [Topology Appl. 154 (2007) 358-362]

We correct the proof of Theorem 8 in “Normality and countable paracompactness of hyperspaces of ordinals” [Topology Appl. 154 (2007) 358-362].     

A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement

We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. We positively answer a question of the strongly paracompact property.     

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.

     

GO-空间乘积的子空间的正交紧性

证明了 GO-空间子空间的正交紧性和弱子正交紧性是等价的 .     

Strong paracompactness and multi-selections

We characterize strong paracompactness in terms of usco multi-selections for closed-valued lower semi-continuous mappings into completely metrizable spaces, thus generalizing recent results obtained by Choban, Mihaylova and Nedev [M. Choban, E. Mihaylova, S. Nedev, On selections and classes of spaces, Topology Appl. 155 (2008) 797-804]. Related results and applications are achieved as well.     

Monotone versions of countable paracompactness

One possible natural monotone version of countable paracompactness, MCP, turns out to have some interesting properties. We investigate various other possible monotone versions of countable paracompactness and how they are related.     

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。     

Hereditary D-property of function spaces over compacta

It is shown that if is compact then every subspace of is a -space in the sense of E. van Douwen, which positively answers Matveev's question. A connection between the -property and Baturov's and Grothendieck's classical theorems about function spaces over compacta is established.

     

Linearly ordered covers,normality and paracompactness

It is shown that a regular space is collectionwise normal and countably paracompact if every open cover has an open, order cushioned refinement. A sufficient condition for paracompactness, in terms of certain order locally finite covers, is given, and is applied to the problem of the paracompactness of product spaces.     

不可数多个GO-空间乘积的k-仿紧性

证明了不可数多个GO-空间的乘积是k-仿紧空间(相似文献   

有限个GO-空间乘积的遗传集体Hausdorff性(英文)

本文证明了最小线性序紧化中点的共尾数不超过ω₁的有限个GO-空间的乘积是遗传集体Hausdorff空间。     

Normality and paracompactness of the Fell topology

Let be a Hausdorff topological space and the hyperspace of all closed nonempty subsets of . We show that the Fell topology on is normal if and only if the space is Lindelöf and locally compact. For the Fell topology normality, paracompactness and Lindelöfness are equivalent.

     

GO-空间的仿紧性

早在1 95 4年,Gillman和Henriksen就证明了一个GO-空间是仿紧空间的充分必要条件,那么,更一般地,任给一个正则不可数基数κ,GO-空间是κ-仿紧空间的充分必要条件是什么呢?本文回答了这个问题.     

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.     

Normality and countable paracompactness of hyperspaces of ordinals

For an ordinal α, α² denotes the collection of all nonempty closed sets of α with the Vietoris topology and K(α) denotes the collection of all nonempty compact sets of α with the subspace topology of α². It is well known that α² is normal iff cfα=1. In this paper, we will prove that for every nonzero-ordinal α:

(1)

α² is countably paracompact iff cfα≠ω.

(2)

K(α) is countably paracompact.

(3)

K(α) is normal iff, if cfα is uncountable, then cfα=α.

In (3), we use elementary submodel techniques.     

GO-空间乘积正规性的充要条件

本文得到了任意两个GO-空间乘积正规性的一个充要条件.     

GO-空间乘积的子空间仿紧性的充分必要条件

我们知道,GO-空间乘积的子空间不一定仿紧.在2000年,数学家N.Kemoto,K.Tamano和Y.Yajima证明了两个特殊的GO-空间-序数乘积子空间的仿紧性的一个充分必要条件.把这个定理进行了推广,到了两个一般的GO-空间乘积的任意子空间仿紧性的一个充分必要条件.     

Locally bounded set-valued mappings and monotone countable paracompactness

We prove that the following statements are equivalent for a space X: (1) X is monotonically countably paracompact; (2) for every metric space Y there exists an operator Φ assigning to each locally bounded mapping , a locally bounded l.s.c. mapping with ?⊂Φ(?) such that Φ(?)⊂Φ(?^′) whenever ?⊂?^′, where B(Y) is the set of all non-empty closed bounded sets of Y; (3) for every metric space Y, there exist operators Φ and Ψ assigning to each u.s.c. mapping , an l.s.c. mapping and a u.s.c. mapping with ?⊂Φ(?)⊂Ψ(?) such that Φ(?)⊂Φ(?^′) and Ψ(?)⊂Ψ(?^′) whenever ?⊂?^′.