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Characterization and Topological Rigidity of Nöbeling Manifolds

Andrzej Nagórko University of Warsaw, Warsaw, Poland
Available Formats:
Electronic ISBN: 978-0-8218-9872-7
Product Code: MEMO/223/1048.E
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $41.40 Click above image for expanded view Characterization and Topological Rigidity of Nöbeling Manifolds Andrzej Nagórko University of Warsaw, Warsaw, Poland Available Formats:  Electronic ISBN: 978-0-8218-9872-7 Product Code: MEMO/223/1048.E  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$41.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 2232013; 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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Volume: 2232013; 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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