Softcover ISBN:  9781470437152 
Product Code:  MBK/109 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470443054 
Product Code:  MBK/109.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9781470437152 
eBook: ISBN:  9781470443054 
Product Code:  MBK/109.B 
List Price:  $104.00 $81.50 
MAA Member Price:  $93.60 $73.35 
AMS Member Price:  $83.20 $65.20 
Softcover ISBN:  9781470437152 
Product Code:  MBK/109 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470443054 
Product Code:  MBK/109.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9781470437152 
eBook ISBN:  9781470443054 
Product Code:  MBK/109.B 
List Price:  $104.00 $81.50 
MAA Member Price:  $93.60 $73.35 
AMS Member Price:  $83.20 $65.20 

Book Details2017; 165 ppMSC: Primary 57
This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's 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 2dimensional 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, 1dimensional curves of positive area, spacefilling curves (Peano curves), 0dimensional 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 2dimensional 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 RiemannHurwitz Theorem, and the Classification Theorem for Compact 2manifolds. 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 2dimensional spaces that are locally Euclidean, the Schoenflies Theorem characterizing the disk, the Triangulation Theorem for 2manifolds, and the R. L. Moore's Decomposition Theorem so useful in understanding fractal sets.
ReadershipUndergraduate and graduate students and researchers interested in topology.
This item is also available as part of a set: 
Table of Contents

Chapters

The fundamental theorem of algebra

The Brouwer fixed point theorem

Tools

Lebesgue covering dimension

Fat curves and Peano curves

The arc, the simple closed curve, and the Cantor set

Algebraic topology

Characterization of the 2sphere

2manifolds

Arcs in $\mathbb {S}^2$ are tame

R. L. Moore’s decomposition theorem

The open mapping theorem

Triangulation of 2manifolds

Structure and classification of 2manifolds

The torus

Orientation and Euler characteristic

The RiemannHurwitz theorem


Additional Material

Reviews

This is a rich and wellwritten book...in particular recommended as pleasant reading to students interested in geometric topology and the geometrictopological foundations of mathematics.
Bruno Zimmermann, Zentralblatt MATH 
Many readers will be hooked by Cannon's aesthetics and proof exposition, where geometric intuition and topological arguments play leading roles...Cannon's books are worth every cent. I have in the past gifted Hilbert & CohnVoseen and Rademacher and Toeplitz to my students. Now I have Cannon's trio to add to my list of giftables.
Tushar Das, MAA Reviews


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This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's 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 2dimensional 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, 1dimensional curves of positive area, spacefilling curves (Peano curves), 0dimensional 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 2dimensional 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 RiemannHurwitz Theorem, and the Classification Theorem for Compact 2manifolds. 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 2dimensional spaces that are locally Euclidean, the Schoenflies Theorem characterizing the disk, the Triangulation Theorem for 2manifolds, and the R. L. Moore's Decomposition Theorem so useful in understanding fractal sets.
Undergraduate and graduate students and researchers interested in topology.

Chapters

The fundamental theorem of algebra

The Brouwer fixed point theorem

Tools

Lebesgue covering dimension

Fat curves and Peano curves

The arc, the simple closed curve, and the Cantor set

Algebraic topology

Characterization of the 2sphere

2manifolds

Arcs in $\mathbb {S}^2$ are tame

R. L. Moore’s decomposition theorem

The open mapping theorem

Triangulation of 2manifolds

Structure and classification of 2manifolds

The torus

Orientation and Euler characteristic

The RiemannHurwitz theorem

This is a rich and wellwritten book...in particular recommended as pleasant reading to students interested in geometric topology and the geometrictopological foundations of mathematics.
Bruno Zimmermann, Zentralblatt MATH 
Many readers will be hooked by Cannon's aesthetics and proof exposition, where geometric intuition and topological arguments play leading roles...Cannon's books are worth every cent. I have in the past gifted Hilbert & CohnVoseen and Rademacher and Toeplitz to my students. Now I have Cannon's trio to add to my list of giftables.
Tushar Das, MAA Reviews