共查询到20条相似文献,搜索用时 843 毫秒
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Angelo Bella 《Topology and its Applications》2009,156(7):1241-1252
A space X is selectively separable if for every sequence of dense subspaces of X one can select finite Fn⊂Dn so that is dense in X. In this paper selective separability and variations of this property are considered in two special cases: Cp spaces and dense countable subspaces in κ2. 相似文献
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Alicia Santiago-Santos 《Topology and its Applications》2011,158(16):2125-2139
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Kaori Yamazaki 《Topology and its Applications》2006,153(15):2805-2814
It is well known that every pair of disjoint closed subsets F0,F1 of a normal T1-space X admits a star-finite open cover U of X such that, for every U∈U, either or holds. We define a T1-space X to be strongly base-normal if there is a base B for X with |B|=w(X) satisfying that every pair of disjoint closed subsets F0,F1 of X admits a star-finite cover B′ of X by members of B such that, for every B∈B′, either or holds. We prove that there is a base-normal space which is not strongly base-normal. Moreover, we show that Rudin's Dowker space is strongly base-(collectionwise)normal. Strong zero-dimensionality on base-normal spaces are also studied. 相似文献
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Feng Tan 《Topology and its Applications》2011,158(3):533-541
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A.V. Ivanov 《Topology and its Applications》2010,157(3):517-521
We construct, assuming the continuum hypothesis, an example of nonmetrizable n-dimensional Cantor manifold Xn(n∈N) with the following properties: 1) is hereditarily separable for all k∈N; 2) is perfectly normal for every k∈N; 3) the space F(Xn) is hereditarily normal for every seminormal functor F that preserves weights and one-to-one points and such that sp(F)={1,k}; in particular, and λ3Xn are hereditarily normal. This example is a generalization of famous Gruenhage's example given in Gruenhage and Nyikos (1993) [4]. 相似文献
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We study conditions under which the Hausdorff quasi-uniformity UH of a quasi-uniform space (X,U) on the set P0(X) of the nonempty subsets of X is bicomplete.Indeed we present an explicit method to construct the bicompletion of the T0-quotient of the Hausdorff quasi-uniformity of a quasi-uniform space. It is used to find a characterization of those quasi-uniform T0-spaces (X,U) for which the Hausdorff quasi-uniformity of their bicompletion on is bicomplete. 相似文献
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Liang-Xue Peng 《Topology and its Applications》2010,157(2):378-876
In this note, we comment on D-spaces, linearly D-spaces and transitively D-spaces. We show that every meta-Lindelöf space is transitively D. If X is a weak -refinable TD-scattered space, then X is transitively D, where TD is the class of all transitively D-spaces. If X is a weak -refinable -scattered space, then X is a D-space, where is the class of all D-spaces, and hence every weak -refinable (or submetacompact) scattered space is a D-space. This gives a positive answer to a question mentioned by Martínez and Soukup. In the last part of this note, we show that if X is a weak -refinable space then X is linearly D. 相似文献
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A metric space (X,d) is called an Atsuji space if every real-valued continuous function on (X,d) is uniformly continuous. It is well known that an Atsuji space must be complete. A metric space (X,d) is said to have an Atsuji completion if its completion is an Atsuji space. In this paper, we study twenty-nine equivalent characterisations for a metric space to have an Atsuji completion. 相似文献
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Piotr Niemiec 《Topology and its Applications》2007,154(3):655-664
The aim of this paper is to answer the following question: let (X,?) and (Y,d) be metric spaces, let A,B⊂Y be continuous images of the space X and let be a fixed continuous surjection. When is the inequality
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Ziqin FengPaul Gartside 《Topology and its Applications》2011,158(9):1124-1130
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