函数空间的拓扑结构

本书是一本深入研究无 限维函数空间拓扑结构的全 新专著。它系统性地总结了 过去二十年来（包括作者和 其他学者）的相关研究成果 ，尤其着重于一些具有实际 背景的函数空间及其对偶空 间的拓扑结构。这本书在拓 扑学的细分领域中具有突出 的贡献，整理并呈现了多位 作者团队及其他学者的研究 成果，是当前拓扑学研究的 重要资料。此书中涵盖的内 容不仅适合拓扑学及泛函分 析的学术研究者使用，也对 应用数学和相关领域的学者 有重要参考价值。是一本创 新性强且学术价值突出的数 学专著，具有广泛的学术应 用潜力。

Preface by J. van Mill Preface Overview 1 Basic Theory 1.1 Preliminaries 1.2 Several theorems in general topology 1.3 ARs and ANRs 1.4 Z-sets and strong Z-sets 1.5 Homotopy denseness and SDAP 1.6 Absorbing sets and coabsorbing sets 1.7 Characterizations for some classical spaces Note for Chapter 2 Topological Structures of Hyperspaces 2.1 Hyperspaces 2.2 Hyperspace theorem for Vietoris topology 2.3 Hyperspace theorem for Fell topology 2.4 Supplements and problems about hyperspaces Note for Chapter 3 Function Spaces with Endograph Fell Topology 3.1 Properties of function spaces with Endograph Fell topology 3.2 Conditions for being metrizable of USC(X,I) 3.3 Conditions for being metrizable of continuous function spaces 3.4 A compacti?cation of metrizable continuous function space 3.5 Borel complexity and Baire property of space of continuous functions 3.6 Strong universality of continuous function space, Ⅰ 3.7 Strong universality of continuous function space, Ⅱ 3.8 Topological structures of function spaces 3.9 Remarks and problems about continuous maps 3.10 Appendix: Baire property Note for Chapter 4 Topological Structures of Spaces of Fuzzy Numbers 4.1 Metrics on set of fuzzy numbers 4.2 Compactness and completeness of spaces of fuzzy numbers 4.3 Spaces of fuzzy numbers are ARs 4.4 Topological structures with endograph metric and Lp metrics 4.5 Topological structures with sendograph metric and L∞ metrics, Ⅰ 4.6 Topological structures with sendograph metric and L∞ metrics, Ⅱ 4.7 Remarks and problems about fuzzy numbers Note for Chapter 5 Function Spaces Coming from Probability Theory 5.1 Spaces of copulas and subcopulas 5.2 Spaces of copulas and exchange copulas 5.3 Topological structure of space of subcouplas 5.4 Remarks and problems about spaces of copulas Note for Chapter 6 Function Spaces Coming from Dynamical Systems 6.1 Box maps on closed intervals 6.2 Function spaces related to topological entropy 6.3 Topological structures of function spaces of transitive maps 6.4 Remarks and problems about spaces related to dynamical systems Note for Chapter 7 Function Spaces Coming from Metric Measure Spaces 7.1 Basic knowledge on metric measure spaces 7.2 Topological structures of spaces of uniformly continuous functions 7.3 Pair of spaces on metric measure spaces 7.4 Remarks and problems about metric measure spaces Note for Chapter References Index on Symbols Index on Subjects