Modern Dimension Theory

Chapter I. Introduction I.1 Coverings I.2. Metrization I.3. Mappings I.4. DimensionChapter 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 FamiliesChapter 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 MappingsChapter IV. Dimension of Separable Metric Spaces IV.1. Cantor Manifolds IV.2. Dimension of En IV.3. Some Theorems in Euclidean Space IV.4. Imbedding IV.5. Є-mappings IV.6. Dimension and Measure IV.7. Dimension and the Ring of Continuous FunctionsChapter 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 DimensionChapter 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 TheoremChapter 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 MappingsChapter 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 HomologyBibliographyIndex