LIST OF SYMBOLS 5
INTRUODUCTION 9
1．(Generalized) topological spaces 13
2．Neighborhood spaces 15
3．Accumulation points;interior,exterior and boundary of a set;closed sets and open sets 18
Characterization of neighborhood spaces by means of a generalized topology 19
Neighborhood spaces whose neighborhood bases consist of open neighborhoods 21
4．Topological spaces 22
5．Topological base 31
6．Continuous mappings of a space into a space;homeomorphisms 34
7．Topologization of a set of by a mapping 41
Subspaces 45
Topological product 48
Topological quotient 52
8．Separation axioms;classification of spaces by means of the separation axioms 52
9．Topologization of a set by means of a real distance;metric spaces 62
Uniformly continuous mappings of a metric space into a metric space 70
Several examples of metric spaces 73
Geodesic metric 74
Normed linear,or vector,spaces 76
Metrization of topological spaces 77
10．Topologizatoin of a set by the uniform topology;Efremovich＇s proximity spaces or δ-spaces 85
Mappings of a δ-space into a δ-space;δ-functions;δ-homeomorphisms (equimorphisms) 96
Metrization of a δ-space 98
11．Topologization of a set by means of the uniform topology;Weil uniform spaces 100
Mappings of uniform spaces into uniform spaces;μ-functions and uniform homeomorphisms 109
Uniformizable spaces 110
Metrization of uniform spaces 115
Tukey-Smirnov uniformities;relation between δ-spaces and uniform spaces 116
Shvarts uniformities 119
12．Topologization of a set by means of an abstract distance 121
Abstract distance and neighborhood spaces 121
Abstract distance and topological spaces 124
Abstract distance and uniform spaces 126
The Kurepa class of spaces E [M] 128
Spaces I (Wa) 131
R-spaces 132
eT-spaces 136
Continuous mappings of spaces defined by an abstract distance 138
Topologization of a set by means of a partially ordered distance 140
Partially ordered distance in the sense of Appert＇s definition 140
Colmez partially ordered distance 142
Topologization of a set by a totally ordered distance;pseuo-distancial,or Kurepa-Fréchet,spaces 146
The Kurepa class of spaces (Da) 149
LITERATURE 151
INDEX 157