Includes bibliographical references (pages 289-305) and index.

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Front Cover; Dimension Theory; Copyright Page; Contents; Preface; Chapter 1. Dimension Theory of Separable Metric Spaces; 1.1. Definition of the small inductive dimension; 1.2. The separation and enlargement theorems for dimension 0; 1.3. The sum, Cartesian product, universal space, compactification and embedding theorems for dimension 0; 1.4. Various kinds of disconnectedness; 1.5. The sum, decomposition, addition, enlargement, separation and Cartesian product theorems; 1.6. Definitions of the large inductive dimension and the covering dimension. Metric dimension.

1.7. The compactification and coincidence theorems. Characterization of dimension in terms of partitions1.8. Dimensional properties of Euclidean spaces and the Hilbert cube. Infinite-dimensional spaces; 1.9. Characterization of dimension in terms of mappings to spheres. Cantor-manifolds. Cohomological dimension; 1.10. Characterization of dimension in terms of mappings to polyhedra; 1.11. The embedding and universal space theorems; 1.12. Dimension and mappings; 1.13. Dimension and inverse sequences of polyhedra.; 1.14. Dimension and axioms; Chapter 2. The Large Inductive Dimension.

2.1. Hereditarily normal and strongly hereditarily normal spaces2.2. Basic properties of the dimension Ind in normal and hereditarily normal spaces; 2.3. Basic properties of the dimension Ind in strongly hereditarily normal spaces; 2.4. Relations between the dimensions ind and Ind . Cartesian product theorems for the dimension Ind; Chapter 3. The Covering Dimension; 3.1. Basic properties of the dimension dim in normal spaces. Relations between the dimensions ind, Ind and dim; 3.2. Characterizations of the dimension dim in normal spaces. Cartesian product theorems for the dimension dim.

3.3. The compactification and the universal space theorems for the dimension dim. The dimension dim and inverse systems of compact spacesChapter 4. Dimension Theory of Metrizable Spaces; 4.1. Basic properties of dimension in metrizable spaces; 4.2. Characterizations of dimension in metrizable spaces. The universal space theorem; 4.3. Dimension and mappings in metrizable spaces; Bibliography; List of special symbols; Author index; Subject index.

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.

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