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The main purpose of this paper is to establish the mapping relation between metric spaces and sn-metric spaces. 相似文献
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If X is a space that can be mapped onto a metric space by a one-to-one mapping, then X is said to have a weaker metric topology.
In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces
with a weaker metric topology. The main results are that
(1) Y is a sequence-covering compact image of a space with a weaker metric topology if and only if Y has a sequence
of point-finite cs-covers such that
for each y ∈ Y.
(2) Y is a sequentially-quotient compact image of a space with a weaker metric topology if and only if Y has a sequence
of point-finite cs*-covers such that
for each y ∈ Y.
Supported by the NNSF(10471084) of China. 相似文献
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本文主要讨论了度量空间的序列覆盖边界紧映象.用序列商、序列覆盖或1-序列覆盖的纤维边界紧或有限来刻画具有sn网或弱基的空间.主要结果如下:(1)度量空间上的序列覆盖边界紧映射是1-序列覆盖映射;(2)空间X是度量空间的序列商边界紧映象当且仅当X是snf-第一可数空间;(3)空间X是度量空间的序列覆盖边界紧S映象当且仅当X有点可数sn-网. 相似文献
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本文利用序列覆盖分层强紧映射,建立了( )-空间,g-可度量空间与特定的度量空间的关系,这是对Alexandroff的部分问题的肯定回答。 相似文献
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局部可分度量空间的序列覆盖s象 总被引:10,自引:0,他引:10
本文给出了局部可分度量空间的1序列覆盖s象,2序列覆盖s象,强序列覆盖s象,序列覆盖s象及子序列覆盖s象的内在刻划.从而使关于对度量空间的各类s象的内在刻划方面的研究更趋于完整. 相似文献
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In this paper, we prove that a space X is a g-metrizable space if and only if X is a weak-open, π and σ-image of a semi-metric space, if and only if X is a strong sequence-covering, quotient, π and mssc-image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.
This project was supported by NNSF of China (No. 10571151 and 10671173). 相似文献
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让ψ是蕴含仿紧性的映射保持的闭遗传性质.本文建立了仿紧局部ψ空间的闭映象、某些序列覆盖L映象的内在特征的一般性定理,推广了仿紧局部紧空间映象等的若干结论. 相似文献
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Shaowen Li 《Czechoslovak Mathematical Journal》2005,55(3):803-808
In this paper, we give the mapping theorems on
-spaces and g-metrizable spaces by means of some sequence-covering mappings, mssc-mappings and π-mappings. 相似文献