
Contents (93 KB) 
v 

Preface 
viii 

Preface to the revised edition 
ix 




Chapter I: Introduction (293 KB) 

I.1 
Coverings 
1 
I.2 
Metrization 
4 
I.3 
Mappings 
7 
I.4 
Dimension 
8 




Chapter II: Dimension of Metric Spaces (626 KB) 

II.1 
Lemmas to sum theorem 
10 
II.2 
Sum theorem 
12 
II.3 
Decomposition theorem 
16 
II.4 
Product theorem 
17 
II.5 
Strong inductive dimension and covering dimension 
20 
II.6 
Some theorems characterizing dimension 
25 
II.7 
The rank of a covering 
28 
II.8 
Normal families 
31 




Chapter III: Mappings and Dimension (741 KB) 

III.1 
Stable value 
35 
III.2 
Extensions of mappings 
37 
III.3 
Essential mappings 
39 
III.4 
Some lemmas 
43 
III.5 
Continuous mappings which lower dimension 
46 
III.6 
Continuous mappings which raise dimension 
49 
III.7 
Baire's zerodimension spaces 
51 
III.8 
Uniformly zerodimensional mappings 
55 




Chapter IV: Dimension of Separable Metric Spaces (863 KB) 

IV.1 
Cantor manifolds 
62 
IV.2 
Dimension of E^{n} 
65 
IV.3 
Some theorems in Euclidean space 
68 
IV.4 
Imbedding 
69 
IV.5 
Epsilonmappings 
74 
IV.6 
PontrjaginSchnirelmann's theorem 
76 
IV.7 
Dimension and measure 
81 
IV.8 
Dimension and the ring of continuous functions 
86 




Chapter V: Dimension and Metrization (675 KB) 

V.1 
Characterization of dimension by a sequence of coverings 
93 
V.2 
Length of coverings 
98 
V.3 
Dimension and metric function 
102 
V.4 
Another metric that characterizes dimension 
114 




Chapter VI: InfiniteDimensional Spaces (835 KB) 

VI.1 
Countabledimensional spaces 
125 
VI.2 
Imbedding of countabledimensional spaces 
132 
VI.3 
Mappings and countabledimensional spaces 
139 
VI.4 
Transfinite inductive dimension 
141 
VI.5 
Sum theorem for transfiniteinductive dimension 
148 
VI.6 
General imbedding theorem 
154 




Chapter VII: Dimension of NonMetrizabel Spaces (1170 KB) 

VII.1 
Sum theorem and subspace theorem for dim 
158 
VII.2 
Dimensions of nonmetrizable spaces 
165 
VII.3 
Sum theorem and subspace theorem for Ind 
170 
VII.4 
Characterization of dim by partitions 
179 
VII.5 
Dimension and mappings 
182 
VII.6 
Product theorem 
192 
VII.7 
Characterization by Δ_{k}(X) 
203 
VII.8 
Characterizations in terms of C(X) 
207 




Chapter VIII: Dimension and Cohomology (841 KB) 

VIII.1 
Homology group and cohomology group of a complex 
213 
VIII.2 
Cohomology group of a topological space 
225 
VIII.3 
Dimension and cohomology 
228 
VIII.4 
Dimension and homology 
239 




Bibliography (984 KB) 
245 

Additional Bibliography 
258 

List of Theorems 
270 

List of Definitions 
273 

Author index 
275 

Subject index 
281 