共查询到19条相似文献,搜索用时 500 毫秒
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局部可数集族、局部有限集族与Alexandroff问题 总被引:9,自引:0,他引:9
本文引进分层强s-映射和分层强紧映射建立具有σ-局部可数网、具有σ-局部可数k-网、具有σ-局部可数基的正则空间以及σ-空间、-空间、g-可度量空间和确定的度量空间之间的联系.这些都是对Alexandroff问题的回答. 相似文献
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本文利用msss-映射,建立了具有σ-局部可数cs-网的空间和具有σ-局部可数弱基的空间与度量空间的关系,这是对Alexandroff的部分的肯定回答。 相似文献
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利用σ-映射建立了具有σ-局部有限cs-网、σ-局部有限cs*-网、σ-局部有限序列邻域网、σ-局部有限序列开网的空间与度量空间确定的σ-映象之间的联系. 相似文献
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关于R-商、ss-映射 总被引:5,自引:0,他引:5
本文借助于R-商、ss-映射建立具有局部可数k-网的k_R-空间(具有由紧子集组成的局部可数k-网的k_R-空间)和度量空间(局部紧度量空间)之间的联系。 相似文献
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关于局部可数网与ss映射 总被引:6,自引:0,他引:6
本文建立了度量空间在几类序列覆盖ss映射下象空间的特征,讨论了局部可数集族与局部可数基(弱基)之间的相互关系,特别地证明了几类具有特定性质的局部可数网的正则空间与度量空间的几类序列覆盖ss映象之间相互等价,回答了Tanaka提出的一个问题. 相似文献
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本文给出了两类局部紧空间闭L(Lindelof)映象的内部特征,证明了空间X是仿紧局部紧空间的闭L映象当且发X是具有σ-局部有限k系的k空间,由此得到在k′空间类中,偏紧局部紧空间的闭L映象等价于偏紧局部紧空间的商SLJ央象,同时不证明了空间X是局部紧度量空间的闭L映象当且X是具有σ-局部有限紧k网的Frechet空间。 相似文献
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该文讨论局部可分度量空间闭s映象的分解定理, 证明了正则的Fréchet空间是局部可分度量空间的闭s映象当且仅当满足如下条件: 具有点可数的cs*网, 第一可数的闭子空间是局部可分的, 且Lindelof的闭子空间是可分的. 相似文献
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Z. Balogh 《Topology and its Applications》1984,17(2):199-215
In this paper the structure of hereditarily strong Σ-spaces (hsΣ-spaces, for short) is dealt with. The main result asserts that an hsΣ-space is the disjoint union of two σ subspaces one of which is an Fσ, the other a Gδ subset. Examples are given that in many ways, this decomposition cannot be improved. Then we investigate the question when an hsΣ-space is a σ-space. It is shown that a GO-space (or a first countable compactum) is metrizable iff it is an hsΣ-space, thereby proving a conjecture of J. van Wouwe. σ-spaces are characterized as being identical with perfect hsΣ-spaces. The question whether a Lindelöf, first countable hsΣ-space is a σ-space is shown to be independent of set theory. A characterization of hsΣ-spaces with no compact subsets of cardinality >2ω is given. 相似文献
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本文得到了σ空间的伪开L映象是σ空间的充分且必要条件,改进了1978年Chaber关于σ空间的映射定理,证明了k半层空间的伪开紧映象是σ空间,深化了1971年Henry关于层空间的映射定理,肯定地回答了1990年林寿关于N空间映射性质的一个问题,同时给出几个例子说明这是σ空间和k半层空间较好的伪开映射定理。 相似文献
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具有σ局部有限sn网的正则空间称为sn可度量化空间,本文讨论了k半层空间的可扩性质,证明了序列覆盖的闭映射保持sn可度量化空间,同时给出与sn可度量化空间的映射性质相关的几个例子。 相似文献
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In this paper,spaces with a locally countable sn-network are discussed.It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network.As its application,almost-open and closed mappings(or finite-to-one and closed mapping) preserve locally countable sn-networks,and a perfect preimage theorem on spaces with a locally countable sn-network is established. 相似文献
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A class of Baire spaces, which contains many known examples and variations thereof, is described and it is shown that no space in this class contains a dense metrizable Gδ-subspace. This gives a class of semi-metrizable spaces which are not σ-spaces. We discuss the existence of Lindelöf semi-metrizable spaces which are not σ-spaces. This is of interest since the only known examples require the use of CH. 相似文献
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本文研究了(LM)-空间(即:可尺度局部凸空间序列的诱导极限)中,Re-takh’s条件(M)与序列式回缩性之间的关系,给出了满足Retakh’s条件(M)的(LM)-空间为序列式回缩的一系列特征条件. 相似文献
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C. M. Pareek 《Acta Mathematica Hungarica》2000,89(3):253-257
It is proved that in a T
3 space countable closed sets have countable character if and only if the set of limit point of the space is a countable compact set and every compact set is of countable character. Also, it is shown that spaces where countable sets have countable character are WN-spaces and are very close to M-spaces. Finally, some questions of Dai and Lia are discussed and some questions are proposed. 相似文献
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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
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