函數空間的拓撲結構 楊忠強 楊寒彪 鄔恩信 9787523219621 【台灣高等教育出版社】

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書名：函數空間的拓撲結構
ISBN：9787523219621
出版社：世界圖書出版
著編譯者：楊忠強 楊寒彪 鄔恩信
頁數：305
所在地：中國大陸 *此為代購商品
書號：1719475
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內容簡介

本書是一本深入研究無限維函數空間拓撲結構的全新專著。它系統性地總結了過去二十年來（包括作者和其他學者）的相關研究成果，尤其著重於一些具有實際背景的函數空間及其對偶空間的拓撲結構。這本書在拓撲學的細分領域中具有突出的貢獻，整理並呈現了多位作者團隊及其他學者的研究成果，是當前拓撲學研究的重要資料。此書中涵蓋的內容不僅適合拓撲學及泛函分析的學術研究者使用，也對應用數學和相關領域的學者有重要參考價值。是一本創新性強且學術價值突出的數學專著，具有廣泛的學術應用潛力。

目錄

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

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