| 书目名称 | Generalized Metric Spaces and Mappings | | 编辑 | Shou Lin,Ziqiu Yun | | 视频video | | | 概述 | This is the first book on generalized metrizable spaces.This is the first book to achieve the classification of spaces by means of mappings.Suitable as a text book for graduate students or senior unde | | 丛书名称 | Atlantis Studies in Mathematics | | 图书封面 |  | | 描述 | The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". .Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.. | | 出版日期 | Book 2016 | | 关键词 | Topological space; Generalized metric space; Metrizable space; Continuous mapping; Paracompact space; Cov | | 版次 | 1 | | doi | https://doi.org/10.2991/978-94-6239-216-8 | | isbn_ebook | 978-94-6239-216-8Series ISSN 1875-7634 Series E-ISSN 2215-1885 | | issn_series | 1875-7634 | | copyright | Atlantis Press and the author(s) 2016 |
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Front Matter |
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Abstract
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| 2 |
,The Origin of Generalized Metric Spaces, |
Shou Lin,Ziqiu Yun |
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Abstract
In this chapter, we derive most of the generalized metric spaces that will be discussed in this book from three perspectives: distance functions, bases or their extensions and generalized countable compactness. At the same time, we give some simple characterizations of these spaces, describe their basic operation properties, such as hereditary properties, productive properties and properties preserved under topological sums, and discuss their preliminary relationships with some other classes of spaces.
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,Mappings on Metric Spaces, |
Shou Lin,Ziqiu Yun |
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Abstract
We start from the class of metrizable spaces, and to show that quotient mappings, pseudo-open mappings, open mappings and closed mappings really satisfy the requirements of being “nice” mappings. In this chapter, we follow the idea of Alexandroff and look for some important intrinsic properties of images or preimages of metric spaces.
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,Generalized Metric Spaces, |
Shou Lin,Ziqiu Yun |
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Abstract
The basic problem of the principle of mutual classifications of spaces and mappings is that, under which classes of mappings certain topological properties remain unchanged (see Question 2.0.6). One of the central topics of this chapter is to determine the given classes of generalized metric spaces are preserved by which kinds of mappings. Therefore, we must fully investigate various properties of generalized metric spaces. One of the most wonderful content of this chapter i.e. seeking the characterizations of these generalized metric spaces is particularly important.
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Back Matter |
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Abstract
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发表于 2025-3-21 20:09:56
