Topology of Infinite-Dimensional Manifolds. 1st ed. 2020

種類:

電子ブック

責任表示:

by Katsuro Sakai

出版情報:

Singapore : Springer Nature Singapore : Imprint: Springer, 2020

著者名:

• Sakai, Katsuro.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9789811575754 [9811575754]    

注記:

Chapter 1: Preliminaries and Background Results -- Chapter 2: Fundamental Results on Infinite-Dimensional Manifolds -- Chapter 3: Characterizations of Hilbert Manifolds and Hilbert Cube Manifolds -- Chapter 4: Triangulation of Hilbert Cube Manifolds and Related Topics -- Chapter 5: Manifolds Modeled on Homotopy Dense Subspaces of Hilbert Spaces -- Chapter 6: Manifolds Modeled on Direct Limits and Combinatorial Manifold -- Appendex: PL n-Manifolds and Combinatorial n-Manifolds -- Epilogue -- Bibliography -- Index.
An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the au

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