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Bibliotheca Mathematica, Volume 6: Modern Dimension Theory provides a brief account of dimension theory as it has been developed since 1941, including the principal results of the classical theory for separable metric spaces.
This book discusses the decomposition theorem, Baire's zero-dimensional spaces, dimension of separable metric spaces, and characterization of dimension by a sequence of coverings. The imbedding of countable-dimensional spaces, sum theorem for strong inductive dimension, and cohomology group of a topological space are also elaborated. This text likewise covers the uniformly zero-dimensional mappings, theorems in euclidean space, transfinite inductive dimension, and dimension of non-metrizable spaces.
This volume is recommended to students and specialists researching on dimension theory.
Chapter I. Introduction
Chapter II. Dimension of Metric Spaces
II.1. The Lemmas to the Sum Theorem
II.2. The Sum Theorem
II.3. The Decomposition Theorem
II.4. The Product Theorem
II.5. The Strong Inductive Dimension and the Covering Dimension
II.6. Some Theorems Characterizing Dimension
II.7. Rank of Coverings
II.8. Normal Families
Chapter III. Mappings and Dimension
III.1. Stable Value
III.2. Extensions of Mappings
III.3. Essential Mappings
III.4. Continuous Mappings which Lower Dimension
III.5. Continuous Mappings which Raise Dimension
III.6. Baire's Zero-Dimensional Spaces
III.7. Uniformly Zero-Dimensional Mappings
Chapter IV. Dimension of Separable Metric Spaces
IV.1. Cantor Manifolds
IV.2. Dimension of En
IV.3. Some Theorems in Euclidean Space
IV.6. Dimension and Measure
IV.7. Dimension and the Ring of Continuous Functions
Chapter V. Dimension and Metrization
V.l. Characterization of Dimension by a Sequence of Coverings
V.2. Length of Coverings
V.3. Dimension and Metric Function
V.4. Another Metric that Characterizes Dimension
Chapter VI. Infinite-Dimensional Spaces
VI.1. Countable-Dimensional Spaces
VI.2. Imbedding of Countable-Dimensional Spaces
VI.3. Transfinite Inductive Dimension
VI.4. General Imbedding Theorem
Chapter VII. Dimension of Non-Metrizable Spaces
VII.1. The General Sum Theorem
VII.2. Dimension of Non-Metrizable Spaces
VII.3. The Sum theorem for Strong Inductive Dimension
VII.4. Dimension and Mappings
Chapter VIII. Dimension and Cohomology
VIII.1. Homology Group and Cohomology Group of a Complex
VIII.2. Cohomology Group of a Topological Space
VIII.3. Dimension and Cohomology
VIII.4. Dimension and Homology
- No. of pages:
- © North Holland 1965
- 1st January 1965
- North Holland
- eBook ISBN:
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