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Characterizing K-Dimensional Universal Menger Compacta.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 1988Copyright date: ©1988Edition: 1st edDescription: 1 online resource (121 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470408008
Subject(s): Genre/Form: Additional physical formats: Print version:: Characterizing K-Dimensional Universal Menger CompactaDDC classification:
  • 514/.3
LOC classification:
  • QA611.28 -- .B478 1988eb
Online resources:
Contents:
Intro -- TABLE OF CONTENTS -- INTRODUCTION -- DEFINITIONS AND NOTATION -- 1. PARTITIONS -- 1.1. Partitions on Compact PL-Manifolds (With Boundary) -- 1.2. The Standard Construction of the Universal k-Dimensional Menger Space μ[sup(k)] and μ[sup(k)]-Manifolds -- 1.3. A Combinatorial Characterization of μ[sup(k)] -- 2. BASIC MOVES -- 2.1. On LC[sup(k-1)]-Spaces and UV[sup(k-1)]-Maps -- 2.2. The Isotopy Move and Verification of Axiom 1 -- 2.3. Absorbing Maps and Basic Properties of μ[sup(k)]-Manifolds -- 2.4. Building Partitions and Associated Maps -- 2.5. Connecting Intersections -- 2.6. Correct Ordering -- 2.7. Increasing the Connectivity of Partition Elements -- 2.8 Some Easy Consequences -- 3. THE Z-SET UNKNOTTING THEOREM -- 3.1. The Z-set Unknotting Theorem -- 3.2. Homogeneity of μ[sup(k)] -- 4. THE DECOMPOSITION THEORY OF MENGER MANIFOLDS -- 4.1. The Z-set Shrinking Theorem -- 4.2. The σ-Z-set Shrinking Theorem -- 4.3. The Main Shrinking Theorem -- 5. THE CHARACTERIZATION THEOREM -- 5.1. The Resolution Theorem -- 5.2. The Characterization Theorem -- 6. NONCOMPACT MENGER MANIFOLDS -- APPENDIX -- LIST OF REFERENCES.
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Intro -- TABLE OF CONTENTS -- INTRODUCTION -- DEFINITIONS AND NOTATION -- 1. PARTITIONS -- 1.1. Partitions on Compact PL-Manifolds (With Boundary) -- 1.2. The Standard Construction of the Universal k-Dimensional Menger Space μ[sup(k)] and μ[sup(k)]-Manifolds -- 1.3. A Combinatorial Characterization of μ[sup(k)] -- 2. BASIC MOVES -- 2.1. On LC[sup(k-1)]-Spaces and UV[sup(k-1)]-Maps -- 2.2. The Isotopy Move and Verification of Axiom 1 -- 2.3. Absorbing Maps and Basic Properties of μ[sup(k)]-Manifolds -- 2.4. Building Partitions and Associated Maps -- 2.5. Connecting Intersections -- 2.6. Correct Ordering -- 2.7. Increasing the Connectivity of Partition Elements -- 2.8 Some Easy Consequences -- 3. THE Z-SET UNKNOTTING THEOREM -- 3.1. The Z-set Unknotting Theorem -- 3.2. Homogeneity of μ[sup(k)] -- 4. THE DECOMPOSITION THEORY OF MENGER MANIFOLDS -- 4.1. The Z-set Shrinking Theorem -- 4.2. The σ-Z-set Shrinking Theorem -- 4.3. The Main Shrinking Theorem -- 5. THE CHARACTERIZATION THEOREM -- 5.1. The Resolution Theorem -- 5.2. The Characterization Theorem -- 6. NONCOMPACT MENGER MANIFOLDS -- APPENDIX -- LIST OF REFERENCES.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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