1.杨忠强是国内拓扑学领域的知名教授，研究领域为无限维拓扑学，一般拓扑学，拓扑动力系统等，曾获陕西省政府科技进步一等奖，4次主持国家自然科学面上项目，4次主持省部级自然科学面上项目，2次获得中国国家留学基金委资助赴外研究。
2. 书中凝聚了作者团队二十多年的研究成果，不仅总结了已知理论，更提出了许多创新性的见解和方法，为相关领域的研究者提供了宝贵的参考。
3. 本书不仅深入探讨了函数空间的拓扑结构，还巧妙地将这些抽象概念与数学的其他分支紧密相连，为读者呈现了一个既深邃又广阔的知识图景。

函数空间的拓扑结构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。

Contents
Preface by J. van Mill iii

Preface v

Overview 1

1 Basic Theory 7
1.1 Preliminaries 7
1.2 Several theorems in general topology 14
1.3 ARs and ANRs 24
1.4 Z-sets and strong Z-sets 34
1.5 Homotopy denseness and SDAP 38
1.6 Absorbing sets and coabsorbing sets 42
1.7 Characterizations for some classical spaces 53
Note for Chapter 1 58

2 Topological Structures of Hyperspaces 61
2.1 Hyperspaces 61
2.2 Hyperspace theorem for Vietoris topology 67
2.3 Hyperspace theorem for Fell topology 71
2.4 Supplements and problems about hyperspaces 76
Note for Chapter 2 79

3 Function Spaces with Endograph Fell Topology 81
3.1 Properties of function spaces with Endograph Fell topology 81
3.2 Conditions for being metrizable of USC(X,I) 93
3.3 Conditions for being metrizable of continuous function spaces 97
3.4 A compacti?cation of metrizable continuous function space 106
3.5 Borel complexity and Baire property of space of continuous functions 111
3.6 Strong universality of continuous function space, I 121
3.7 Strong universality of continuous function space, II 132
3.8 Topological structures of function spaces 141
3.9 Remarks and problems about continuous maps 142
3.10 Appendix: Baire property 145
Note for Chapter 3 151

4 Topological Structures of Spaces of Fuzzy Numbers 153
4.1 Metrics on set of fuzzy numbers 154
4.2 Compactness and completeness of spaces of fuzzy numbers 160
4.3 Spaces of fuzzy numbers are ARs 167
4.4 Topological structures with endograph metric and Lp metrics 176
4.5 Topological structures with sendograph metric and L∞ metrics, I 186
4.6 Topological structures with sendograph metric and L∞ metrics, II 192
4.7 Remarks and problems about fuzzy numbers 201
Note for Chapter 4 204

5 Function Spaces Coming from Probability Theory 207
5.1 Spaces of copulas and subcopulas 207
5.2 Spaces of copulas and exchange copulas 216
5.3 Topological structure of space of subcouplas 221
5.4 Remarks and problems about spaces of copulas 226
Note for Chapter 5 230

6 Function Spaces Coming from Dynamical Systems 233
6.1 Box maps on closed intervals 233
6.2 Function spaces related to topological entropy 239
6.3 Topological structures of function spaces of transitive maps 251
6.4 Remarks and problems about spaces related to dynamical systems 261
Note for Chapter 6 263

7 Function Spaces Coming from Metric Measure Spaces 265
7.1 Basic knowledge on metric measure spaces 265
7.2 Topological structures of spaces of uniformly continuous functions 267
7.3 Pair of spaces on metric measure spaces 275
7.4 Remarks and problems about metric measure spaces 281
Note for Chapter 7 281

References 283

Index on Symbols 297

Index on Subjects 301