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Characterization and Topological Rigidity of Nöbeling Manifolds
Available Formats:
Electronic ISBN: 9780821898727
Product Code: MEMO/223/1048.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
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Characterization and Topological Rigidity of Nöbeling Manifolds
Available Formats:
Electronic ISBN:  9780821898727 
Product Code:  MEMO/223/1048.E 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $41.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 223; 2013; 92 ppMSC: Primary 54;
The author develops a theory of Nöbeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nöbeling manifold characterization conjecture.

Table of Contents

1. Introduction and preliminaries

1. Introduction

2. Preliminaries

2. Reducing the proof of the main results to the construction of $n$regular and $n$semiregular ${\mathcal {N}_{n}}$covers

3. Approximation within an $\mathcal {N}_{n}$cover

4. Constructing closed $\mathcal {N}_{n}$covers

5. Carrier and nerve theorems

6. Anticanonical maps and semiregularity

7. Extending homeomorphisms by the use of a “brick partitionings” technique

8. Proof of the main results

3. Constructing $n$semiregular and $n$regular ${\mathcal {N}_{n}}$covers

9. Basic constructions in $\mathcal {N}_{n}$spaces

10. Core of a cover

11. Proof of theorem


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Volume: 223; 2013; 92 pp
MSC: Primary 54;
The author develops a theory of Nöbeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nöbeling manifold characterization conjecture.

1. Introduction and preliminaries

1. Introduction

2. Preliminaries

2. Reducing the proof of the main results to the construction of $n$regular and $n$semiregular ${\mathcal {N}_{n}}$covers

3. Approximation within an $\mathcal {N}_{n}$cover

4. Constructing closed $\mathcal {N}_{n}$covers

5. Carrier and nerve theorems

6. Anticanonical maps and semiregularity

7. Extending homeomorphisms by the use of a “brick partitionings” technique

8. Proof of the main results

3. Constructing $n$semiregular and $n$regular ${\mathcal {N}_{n}}$covers

9. Basic constructions in $\mathcal {N}_{n}$spaces

10. Core of a cover

11. Proof of theorem
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