Point-countable Covers and Sequence-covering Mappings
Point-countable Covers and Sequence-covering Mappings
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发表时间：
2007
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通讯作者：
Shou Lin
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作者：
Shou Lin
点可数覆盖和序列覆盖映射 林寿 (福建师范大学数学系，福建福州 350007) 摘要 映射和覆盖方法是研究一般拓扑的基本工具。广义度量性质和覆盖性质理论源于可度量性和紧致性的推广，其中很多问题都涉及对某些点可数覆盖的研究。对可数覆盖相关问题的思考导致了 k 网络理论和广义度量空间中度量空间映射的发展。本书总结了近十年来广义度量空间理论的基本任务和重要贡献，并用四章阐述了1993年至2000年关于点可数覆盖和序列覆盖映射的一些成果。第二章重点介绍了点可数覆盖和度量空间的s-映射理论。在第三章中，我们提出了点有限覆盖序列以及度量空间的映射和紧映射理论。第四章讨论遗传性保闭覆盖、支配族和度量空间的闭映射理论。第五章研究了星可数覆盖和局部可分度量空间的商映射理论。
Point-countable Covers and Sequence-covering Mappings Shou LIN (Department of Mathematics, Fujian Normal University, Fuzhou, Fujian 350007, P. R. China) Abstract The method of mappings and covers is a basic tool to study general topology. The theory of generalized metric properties and covering properties stems from a generalization of metrizability and compactness, in which a great many problems involve a research for certain point-countable covers. A deliberation on questions related to point-countable covers leads to a development of the theories of k-networks and mappings of metric spaces in generalized metric spaces. This book summarizes the essential tasks and the important contribution to the theory of generalized metric spaces in the past ten years, and in four chapters expounds some results about point-countable covers and sequence-covering mappings from 1993 to 2000. In the second chapter, we centre on point-countable covers and the theory of s-mappings of metric spaces. In the third chapter, we present a sequence of point-finite covers and the theory of -mappings and compact mappings of metric spaces. In the fourth chapter, we discuss hereditarily closure-preserving covers, dominated families and the theory of closed mappings of metric spaces. In the fifth chapter, we study star-countable covers and the theory of quotient mappings of locally separable metric spaces.