
Preface 
vii 




Chapter 1: Dimension theory of separable metric spaces  
1.1 
Definition of the small inductive dimension 
2 
1.2 
The separation and enlargement theorems for dimension 0 
8 
1.3 
The sum, Cartesian product, universal space, compactification and embedding theorems for dimension 0 
15 
1.4 
Various kinds of disconnectedness 
24 
1.5 
The sum, decomposition, addition, enlargement, separation and Cartesian product theorems 
31 
1.6 
Definitions of the large inductive dimension and the covering dimension. Metric dimension 
40 
1.7 
The compactification and coincidence theorems. Characterization of dimensions in terms of partitions 
47 
1.8 
Dimensional properties of Euclidean spaces and the Hilbert cube. Infinitedimensional spaces 
56 
1.9 
Characterization of dimension in terms of mappings to spheres. Cantormanifolds. Cohomological dimension 
69 
1.10 
Characterization of dimension in terms of mappings to polyhedra 
79 
1.11 
The embedding and universal space theorems 
94 
1.12 
Dimension and mappings 
106 
1.13 
Dimension and inverse sequence of polyhedra 
114 
1.14 
Axioms for dimension 
123 




Chapter 2: The large inductive dimension  
2.1 
Hereditarily normal and strongly hereditarily normal spaces 
127 
2.2 
Basic properties of the dimension Ind in normal and hereditarily normal spaces 
133 
2.3 
Basic properties of the dimension Ind in strongly hereditarily normal spaces 
144 
2.4 
Relations between the dimensions ind and Ind. Cartesian product theorems for the dimension Ind. Dimension Ind and mappings 
155 




Chapter 3: The covering dimension  
3.1 
Basic properties of the dimension dim in normal spaces. Relations between the dimensions ind, Ind and dim 
168 
3.2 
Characterizations of the dimension dim in normal spaces 
182 
3.3 
Dimension dim and mappings 
193 
3.4 
The compactification, universal space and Cartesian product theorems for the dimension dim. Dimension dim and inverse systems of compact spaces 
205 




Chapter 4: Dimension theory of metrizable spaces  
4.1 
Basic properties of dimension in metrizable spaces 
217 
4.2 
Characterizations of dimension in metrizable spaces. The universal space theorems 
228 
4.3 
Dimension and mappings in metrizable spaces 
240 




Chapter 5: Countabledimensional spaces  
5.1 
Definitions and characterizations of countabledimensional and strongly countabledimensional spaces 
253 
5.2 
Basic properties of countabledimensional and strongly countabledimensional spaces 
261 
5.3 
The compactification and universal space theorems for countabledimensional and strongly countabledimensional spaces 
271 
5.4 
Countable dimensionality and mappings 
280 
5.5 
Locally finitedimensional spaces 
288 




Chapter 6: Weakly infinitedimensional spaces  
6.1 
Definition and basic properties of weakly infinitedimensional spaces 
300 
6.2 
An example of a totally disconnected strongly infinitedimensional space 
312 
6.3 
Weak infinite dimensionality and mappings 
316 




Chapter 7: Transfinite dimensions  
7.1 
Definitions and basic properties of the transfinite dimensions trind and trInd 
325 
7.2 
The separation, sum, enlargement, completion and universal space theorems for the transfinite dimensions trind and trInd 
338 
7.3 
Transfinite dimensions trker and trdim 
351 




Bibliography 
365 

List of special symbols 
393 

Author index 
395 

Subject index 
398 