James W. Cannon Topology as Fluid Geometry: Two-Dimensional Spaces, Volume 2 9781470437152

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Автор: James W. Cannon
Название: Topology as Fluid Geometry: Two-Dimensional Spaces, Volume 2
ISBN: 9781470437152
Издательство: Mare Nostrum (Eurospan)
Классификация:

Геометрия

ISBN-10: 1470437155
Обложка/Формат: Paperback
Страницы: 165
Вес: 0.34 кг.
Дата издания: 28.02.2018
Серия: Mathematics
Язык: English
Размер: 254 x 178
Читательская аудитория: Professional and scholarly
Ключевые слова: Geometry,Topology
Подзаголовок: Two-dimensional spaces, volume 2
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Поставляется из: Англии
Описание: This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth centurys masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology.The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two proofs), the No Retraction Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem, the Open Mapping Theorem, the Riemann-Hurwitz Theorem, and the Classification Theorem for Compact 2-manifolds. Volume 2 also includes a number of theorems usually assumed without proof since their proofs are not readily available, for example, the Zippin Characterization Theorem for 2-dimensional spaces that are locally Euclidean, the Schoenflies Theorem characterizing the disk, the Triangulation Theorem for 2-manifolds, and the R. L. Moores Decomposition Theorem so useful in understanding fractal sets.
Дополнительное описание: Geometry|Topology

Topology as Fluid Geometry: Two-Dimensional Spaces, Volume 2, James W. Cannon