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In this paper we examine the interactions between the topology of certain linearly ordered topological spaces (LOTS) and the properties of trees in whose branch spaces they embed. As one example of the interaction between ordered spaces and trees, we characterize hereditary ultraparacompactness in a LOTS (or GO-space) X in terms of the possibility of embedding the space X in the branch space of a certain kind of tree. 相似文献
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Wei-Xue Shi 《Proceedings of the American Mathematical Society》1999,127(2):615-618
In this paper, we prove that if a perfect GO-space has a -discrete dense set, then has a perfect linearly ordered extension. This answers a problem raised by H. R. Bennett, D. J. Lutzer and S. Purisch. And the result is also a partial answer to an old problem posed by H. R. Bennett and D. J. Lutzer.
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Raushan Z. Buzyakova 《Proceedings of the American Mathematical Society》2004,132(7):2171-2181
It is shown that any continuum cleavable over a LOTS is embeddable into .
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本文对“每一个GO-空间都是可数仿紧的”这一性质进行了推广,得到了“每一个GO-空间都是1:x∈[LX-X]}仿紧的”;论证了在一定条件下,一个拓扑空间和一个GO-空间乘积的正规性与这个拓扑空间和一个正则不可数基数的乘积正规性是等价的;并在这两个结论的基础上,又得出了一些重要的定理. 相似文献
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本文是在日本数学家Kemoto 1993年所作的关于一个GO-空间(广义线性序空间)和一个正则不可数基数乘积正规性的结果的基础上作了进一步的推广,得到了两个GO-空间乘积的正规性的一个更一般的结果. 相似文献
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Victor Neumann-Lara 《Topology and its Applications》1988,30(3):225-235
We obtain sufficient conditions for a linearly ordered topological space (LOTS) to be densely orderable. As a consequence we obtain a characterization of those metrizable LOTS with connected ordered compactifications. 相似文献
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In this paper we characterize generalized ordered spaces that are metrizably fibered in terms of certain quotient spaces and in terms of the existence of special open covers. We apply our results to give a new characterization of perfect generalized ordered spaces that have a σ-closed-discrete dense subset and to give examples of GO-spaces that are, or are not, metrizably fibered. 相似文献
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