共查询到20条相似文献,搜索用时 31 毫秒
1.
局部强紧空间的Hoare空间与Smyth空间 总被引:1,自引:0,他引:1
本文主要讨论局部强紧空间的性质,特别是其Hoare空间和Smyth空间的性质,证明了T_0空间为局部强紧空间的当且仅当其Hoare空间为局部强紧空间,局部强紧空间的Smyth空间为C-空间.对于强局部紧空间,我们有类似的结论. 相似文献
2.
Inthispaper,allspacesareregularandT1,andallmappingsarecontinuousandonto .Readersmayreferto [1 ]forunstateddefinitions. Quiterecently ,somecharacterizationsforcertainL imagesofparacompactlocallycompactspaceshavebeenobtainedin [2 ] .Similarly ,wecanestablishthech… 相似文献
3.
主要借助于紧覆盖映射、闭映射和商映射讨论了局部紧Lindel(o)f空间的像空间,推导出具有某些特定性质的k系空间的一些刻画,引入强k系的概念给出了局部紧Lindel(o)f空间和仿紧局部紧空间的一种新的等价刻画. 相似文献
4.
本文利用极大点空间的等价刻划证明了极大点空间的某些子空间、不交和、 乘积空间、逆序列的逆极限、具有可数基的局部紧的Hausdorff空间是极大点空间,还 给出了具有可数基的局部紧的Hausdorff空间的Domain hull. 相似文献
5.
We establish two theorems that refine the classical Stone duality between generalized Boolean algebras and locally compact Boolean spaces. In the first theorem, we prove that the category of left-handed skew Boolean algebras whose morphisms are proper skew Boolean algebra homomorphisms is equivalent to the category of étale spaces over locally compact Boolean spaces whose morphisms are étale space cohomomorphisms over continuous proper maps. In the second theorem, we prove that the category of left-handed skew Boolean -algebras whose morphisms are proper skew Boolean -algebra homomorphisms is equivalent to the category of étale spaces with compact clopen equalizers over locally compact Boolean spaces whose morphisms are injective étale space cohomomorphisms over continuous proper maps. 相似文献
6.
A.V. Arhangel'skii 《Topology and its Applications》2007,154(3):625-634
We introduce a new cardinal invariant, core of a space, defined for any locally compact Hausdorff space X and denoted by cor(X). Locally compact spaces of countable core generalize locally compact σ-compact spaces in a way that is slightly exotic, but still quite natural. We show in Section 1 that under a broad range of conditions locally compact spaces of countable core must be σ-compact. In particular, normal locally compact spaces of countable core and realcompact locally compact spaces of countable core are σ-compact. Perfect mappings preserve the class of spaces of countable core in both directions (Section 2). The Alexandroff compactification aX is weakly first countable at the Alexandroff point a if and only if cor(X)=ω (Section 3). Two examples of non-σ-compact locally compact spaces of countable core are discussed in Section 3. We also extend the well-known theorem of Alexandroff and Urysohn on the cardinality of perfectly normal compacta to compacta satisfying a weak version of perfect normality. Several open problems are formulated. 相似文献
7.
We prove that every locally connected quotient G/H of a locally compact, connected, first countable topological group G by
a compact subgroup H admits a G-invariant inner metric with curvature bounded below. Every locally compact homogeneous space
of curvature bounded below is isometric to such a space. These metric spaces generalize the notion of Riemannian homogeneous
space to infinite dimensional groups and quotients which are never (even infinite dimensional) manifolds. We study the geometry
of these spaces, in particular of non-negatively curved homogeneous spaces.
Dedicated to the memory of A. D. Alexandrov 相似文献
8.
仿紧局部紧空间的序列覆盖L-映象 总被引:9,自引:1,他引:8
本文利用特定的覆盖性质,建立了仿紧局部紧空的序列覆盖L-映象和紧覆盖L-映象的特征,得到或深化了局部紧度量空间的一些相应结果。 相似文献
9.
Frame multiresolution analysis and infinite trees in Banach spaces on locally compact abelian groups
S.S.Panday 《分析论及其应用》2004,20(3):231-241
We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaceson locally compact abelian groups including modulation spaces. 相似文献
10.
Jinjin Li 《Acta Mathematica Hungarica》2004,104(4):301-305
We continue to study the characterizations of paracompact locally compact spaces under certain quotient mappings, and discuss
the relationships among them, which expand the results on certain quotient images of paracompact locally compact spaces.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
11.
A note on closed images of locally compact metric spaces 总被引:1,自引:0,他引:1
Shou Lin 《Acta Mathematica Hungarica》2005,109(1-2):157-162
Summary A decomposition theorem about closed images of locally compact metric spaces is discussed. It is shown that a space is a closed
image of a locally compact metric space if and only if it is a regular Fréchet space with a point-countable k-network, and each of its closed first-countable subset is locally compact. 相似文献
12.
T. E. Khmyleva 《Journal of Mathematical Sciences》1983,22(6):1860-1862
If S is a locally compact metric space, countable at infinity, and the metric space T is not locally compact, then the spaces C(S) and C(T) are not isomorphic. 相似文献
13.
本文利用一致覆盖的概念,讨论了度量空间的序列覆盖紧映象的结构.主要结果有: (1)空间X是局部可分度量空间的序列覆盖紧映象当且仅当X具有由cosmic子空间构成的一致sn网; (2)空间X是局部可分度量空间的序列覆盖,商紧映象当且仅当X是度量空间的序列覆盖,商紧映象且是局部cosmic空间. 相似文献
14.
We prove that there exists a cohomology locally connected compact metrizable space which is not homology locally connected. In the category of compact Hausdorff spaces a similar result was proved earlier by G.E. Bredon. 相似文献
15.
16.
称局部凸空间(E,(?)0)为WCM空间若对于任何弱于(?)0的局部凸拓扑(?),(E,(?))与(E,(?)0)具相同的弱紧圆凸集.本文研究了WCM空间的存在性及其与其他类型局部凸空间之间的关系,还给出了WCM空间的一种映照特征. 相似文献
17.
A generalized notion of regularity is introduced which enables one to study locally compact spaces, sequential spaces, ω-regular spaces, and other diverse types of spaces as special wises of p-regular spaces. 相似文献
18.
Pawel Lurje 《manuscripta mathematica》1974,13(3):309-317
We define locally circled vector groups as topological vector spaces over the discrete real or complex numberfield with a neighbourhoodbase of zero consisting of circled sets. Every topological vector space is a locally circled vector group. Topological vector groups and especially locally circled vector groups have useful applications to topological vector spaces and this paper is intended as an introduction to the theory of locally circled vector groups. Continuations including applications to topological vector spaces will follow. Here we study the structure of finite dimensional and locally compact vector groups, describe those locally circled vector groups which have a generating precompact circled set and finally prove some theorems about convex sets in these spaces. 相似文献
19.
K. Keimel 《Algebra and Logic》2009,48(5):330-343
The majority of categories used in denotational semantics are topological in nature. One of these is the category of stably
compact spaces and continuous maps. Previously, Eilenberg–Moore algebras were studied for the extended probabilistic powerdomain
monad over the category of ordered compact spaces X and order-preserving continuous maps in the sense of Nachbin. Appropriate algebras were characterized as compact convex subsets
of ordered locally convex topological vector spaces. In so doing, functional analytic tools were involved. The main accomplishments
of this paper are as follows: the result mentioned is re-proved and is extended to the subprobabilistic case; topological
methods are developed which defy an appeal to functional analysis; a more topological approach might be useful for the stably
compact case; algebras of the (sub)probabilistic powerdomain monad inherit barycentric operations that satisfy the same equational
laws as those in vector spaces. Also, it is shown that it is convenient first to embed these abstract convex sets in abstract
cones, which are simpler to work with. Lastly, we state embedding theorems for abstract ordered locally compact cones and
compact convex sets in ordered topological vector spaces. 相似文献
20.
Jing Hui QIU 《数学学报(英文版)》2007,23(12):2295-2302
In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact. 相似文献