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函数空间的拓扑结构（英文版）
作者：杨忠强 杨寒彪 邬恩信
出版社：世界图书出版公司
出版时间：2025-01-01
ISBN：9787523219621
定价：¥88.00
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内容简介
Topological Structures of Function Spaces是一本深入研究函数空间的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，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。
作者简介
杨忠强，闽南师范大学二级教授，博士生导师。1990年和1994年分别在四川大学数学系和日本筑波大学数学研究所取得理学博士学位和博士（数学）学位。1989年“格与拓扑”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。研究领域为无限维拓扑学，一般拓扑学，拓扑动力系统，统计学，模糊数学，格上拓扑学，格论等。 杨寒彪，五邑大学副教授，硕士导师，获得日本筑波大学博士学位，主要从事主要研究无限维拓扑学函数空间的研究。主持过国家自然科学基金青年项目1项，天元项目1项目，广东省自然科学基金面上项目1项和博士启动项目1项目，近年来在Topology and its Applications、Open Mathematics等国际数学期刊上发表近十篇论文。 邬恩信，汕头大学副教授，硕士生导师。2012年毕业于加拿大西安大略大学。主持1项国家自然科学青年基金，参加1项国家自然科学基金面上项目。研究领域为拓扑学和几何学，目前主要研究广义流形（diffeology）相关的几何与拓扑及其应用。
目录
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
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
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