Topological Spaces: Including a Treatment of Multi-valued Functions, Vector Spaces, and Convexity

Couverture
Courier Corporation, 1 janv. 1997 - 270 pages
Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition.
 

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Table des matières

Chapter
1
MAPPINGS OF ONE SET INTO ANOTHER
20
ORDERED SETS
28
TOPOLOGICAL SPACES
40
Chapter Page V TOPOLOGICAL PROPERTIES OF METRIC SPACES 1 Topology of a metric space
82
Sums and products of metric spaces
85
Sequences of elements
87
Totally bounded spaces and complete spaces
90
Linear mappings
133
Linear varieties cones convex sets
136
Dimension of a convex set
144
The gauge of a convex set
148
The HahnBanach theorem
154
CONVEX SETS AND CONVEX FUNCTIONS IN THE SPACE R 1 Topological properties of convex sets
158
Simplexes Kakutanis Theorem
168
Matrices
176

Separable sets
93
Compact sets
94
Connected sets
96
curves
99
Singlevalued mappings of one metric space into another
103
MAPPINGS FROM ONE TOPOLOGICAL SPACE INTO ANOTHER 1 Semicontinuous mappings
109
Properties of the two types of semicontinuity
113
Maximum theorem
115
Fixed points of a mapping of R into R
117
Limits of a family of sets
118
Hausdorff metrics
126
MAPPINGS OF ONE VECTOR SPACE INTO ANOTHER 1 Vector spaces
129
Bistochastic matrices
180
Convex functions
188
Differentiable convex functions
194
The fundamental properties of convex functions
200
Quasi convex functions
207
The fundamental inequality of convexity
211
Subo functions
216
Sconvex functions
219
Extremal problems with convex and concave functions
226
Chapter Page
231
INDEX 265

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