一致覆盖和度量空间的紧映象

葛英;林寿

数学学报 ›› 2004, Vol. 47 ›› Issue (6) : 1149-115.

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数学学报 ›› 2004, Vol. 47 ›› Issue (6) : 1149-115. DOI: 10.12386/A2004sxxb0142
论文

一致覆盖和度量空间的紧映象

    葛英;林寿
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Uniform Covers and Compact Images of Metric Spaces

    Ying GE(1), Shou LIN(2)
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摘要

本文利用一致覆盖的概念,讨论了度量空间的序列覆盖紧映象的结构.主要结果有: (1)空间X是局部可分度量空间的序列覆盖紧映象当且仅当X具有由cosmic子空间构成的一致sn网; (2)空间X是局部可分度量空间的序列覆盖,商紧映象当且仅当X是度量空间的序列覆盖,商紧映象且是局部cosmic空间.

Abstract

In this paper the structures of sequence-covering compact images of locally separable metric spaces are investigated by uniform covers, the main results are that (1) a space is a sequence-covering compact image of a locally separable metric space if and only if it has a uniform sn-network consisting of cosmic subspaces; (2) a space is a sequence-covering quotient compact image of a locally separable metric space if and only if it is a locally cosmic space and a sequence-covering quotient compact image of a metric space.

关键词

一致覆盖 / 点星网 / 序列覆盖映射

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葛英;林寿. 一致覆盖和度量空间的紧映象. 数学学报, 2004, 47(6): 1149-115 https://doi.org/10.12386/A2004sxxb0142
Ying GE(1), Shou LIN(2). Uniform Covers and Compact Images of Metric Spaces. Acta Mathematica Sinica, Chinese Series, 2004, 47(6): 1149-115 https://doi.org/10.12386/A2004sxxb0142
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