k-COVERS AND CERTAIN QUOTIENT IMAGES OF PARACOMPACT LOCALLY COMPACT SPACES

We continue to discuss some properties of certain k-covers. As applications, we give some characterizations of certain quotient images of paracompact locally compact spaces.     

局部紧 Lindel(o)f空间的映象

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.     

A note on closed images of locally compact metric spaces

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.     

Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces

We prove that any metrizable non-compact space has a weaker metrizable nowhere locally compact topology. As a consequence, any metrizable non-compact space has a weaker Hausdorff connected topology. The same is established for any Hausdorff space X with a σ-locally finite base whose weight w(X) is a successor cardinal.     

Images of locally compact metric spaces

We establish relationships between locally compact-metric spaces and all kinds of spaces with mk-system (compact k-network) by means of compact-covering mappings, quotient mapping and closed mappings. This revised version was published online in June 2006 with corrections to the Cover Date.     

仿紧局部可分空间及其映象

探讨仿紧局部可分空间的一些性质,获得了两个可度量化定理,建立了仿紧局部可分空间的各类序列覆盖L-映象的特征。     

The Sequence-covering Compact Images of Paracompact Locally Compact Spaces

Ｉｎｔｈｉｓｐａｐｅｒ,ａｌｌｓｐａｃｅｓａｒｅｒｅｇｕｌａｒａｎｄＴ1,ａｎｄａｌｌｍａｐｐｉｎｇｓａｒｅｃｏｎｔｉｎｕｏｕｓａｎｄｏｎｔｏ .Ｒｅａｄｅｒｓｍａｙｒｅｆｅｒｔｏ [1 ]ｆｏｒｕｎｓｔａｔｅｄｄｅｆｉｎｉｔｉｏｎｓ.　Ｑｕｉｔｅｒｅｃｅｎｔｌｙ ,ｓｏｍｅｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｆｏｒｃｅｒｔａｉｎＬ ｉｍａｇｅｓｏｆｐａｒａｃｏｍｐａｃｔｌｏｃａｌｌｙｃｏｍｐａｃｔｓｐａｃｅｓｈａｖｅｂｅｅｎｏｂｔａｉｎｅｄｉｎ [2 ] .Ｓｉｍｉｌａｒｌｙ ,ｗｅｃａｎｅｓｔａｂｌｉｓｈｔｈｅｃｈ…     

Measures with natural spectra on locally compact abelian groups

Every bounded regular Borel measure on noncompact LCA groups is a sum of an absolutely continuous measure and a measure with natural spectrum. The set of bounded regular Borel measures with natural spectrum on a nondiscrete LCA group whose Fourier-Stieltjes transforms vanish at infinity is closed under addition if and only if is compact.

     

The structure of shift invariant spaces on a locally compact abelian group

We investigate shift invariant subspaces of L²(G), where G is a locally compact abelian group. We show, among other things, that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame.     

仿紧局部cosmic空间的一些性质

给出仿紧局部cosmic空间的一些特征,建立了仿紧局部cosmic空间的几类序列覆盖L映象的特征,证明了闭L映射和商ss映射保持仿紧局部cosmic空间的性质,此外,还给出仿紧局部cosmic空间的一些映射性质。     

Open subspaces of locally compact metric spaces

Although classically every open subspace of a locally compact space is also locally compact, constructively this is not generally true. This paper provides a locally compact remetrization for an open set in a compact metric space and constructs a one-point compactification. MSC: 54D45, 03F60, 03F65.     

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.     

On modal logics arising from scattered locally compact Hausdorff spaces

For a topological space X, let $\mathsf{L}(X)$ be the modal logic of X where □ is interpreted as interior (and hence ◇ as closure) in X. It was shown in [3] that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, ${\mathsf{S4}.\mathsf{Grz}}_n$ ($n\ge 1$), and their intersections arise as $\mathsf{L}(X)$ for some Stone space X. We give an example of a scattered Stone space whose logic is not such an intersection. This gives an affirmative answer to [3, Question 6.2]. On the other hand, we show that a scattered Stone space that is in addition hereditarily paracompact does not give rise to a new logic; namely we show that the logic of such a space is either S4.Grz or ${\mathsf{S4}.\mathsf{Grz}}_n$ for some $n\ge 1$. In fact, we prove this result for any scattered locally compact open hereditarily collectionwise normal and open hereditarily strongly zero-dimensional space.     

Diestel-Faires定理在局部凸空间中的推广

通过Banach 空间与局部凸空间的对比,将Banach 空间上的Diestel-Faires 定理在局部凸空间上进行推广。进一步给出了局部凸空间上的Orlicz-Pettis定理与推论。     

Midconvex functions in locally compact groups

The theorems of Bernstein-Doetsch, and Ostrowski, concerning the continuity of midconvex functions are extended to open subsets of locally compact and root-approximable topological groups.

     

On the homology of locally compact spaces with ends

We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original graph-theoretical definition could be captured in the usual language for homology theories, so as to make it applicable to more general spaces. In this paper we provide such a general topological framework: we define a homology theory which satisfies the usual axioms, but which maintains the special role for ends that has made this homology work so well for graphs.     

On the resolvability of locally connected spaces

We solve a problem of Padmavally about resolvability of locally connected spaces, in the case where the space under consideration is regular.

     

Transversality on locally pseudocompact groups

Two non-discrete Hausdorff group topologies \tau and \delta on a group G are called transversal if the least upper bound \tau \vee \delta of \tau and \delta is the discrete topology. In this paper, we discuss the existence of transversal group topologies on locally pseudocompact, locally precompact, or locally compact groups. We prove that each locally pseudocompact, connected topological group satisfies central subgroup paradigm, which gives an affrmative answer to a problem posed by Dikranjan, Tkachenko, and Yaschenko [Topology Appl., 2006, 153:3338-3354]. For a compact normal subgroup K of a locally compact totally disconnected group G, if G admits a transversal group topology, then G/K admits a transversal group topology, which gives a partial answer again to a problem posed by Dikranjan, Tkachenko, and Yaschenko in 2006. Moreover, we characterize some classes of locally compact groups that admit transversal group topologies.     

Persistently unbounded functions on locally compact Abelian groups

This paper deals, given an arbitrary locally compact Abelian group, with the existence of integrable functions all whose convolution powers are essentially unbounded.     

关于局部凸空间的中点局部一致凸性

给出局部凸空间的（弱）中点局部一致凸性,证明了它与（弱）中点局部一致光滑性具有对偶性质,讨论它们与其它凸性之间的关系,推广了Banach空间相应概念和结果.