Amazon no longer offers textbook rentals. We do!

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

by: Berge, Claude

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

by: Berge, Claude

ISBN 13:
9780486696539
ISBN 10:
0486696537
Format: Paperback
Copyright: 09/16/2010
Publisher: Dover Publications

Rent From $10.49

New From $15.79

List Price $15.95 Save

Rent $10.49

TERM	PRICE	DUE
SEMESTER	$11.05	Dec 13
QUARTER	$10.49	Aug 16
SHORT TERM	$10.00	Jul 02

Added Benefits of Renting

Free Shipping Both Ways
Highlight/Take Notes Like You Own It
Purchase/Extend Before Due Date

Add to Cart

List Price $15.95 Save $0.16

New $15.79

Usually Ships in 3-5 Business Days

We Buy This Book Back!

Included with your book

Free Shipping On Every Order

Add to Cart

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Extend or Purchase Your Rental at Any Time

Need to keep your rental past your due date? At any time before your due date you can extend or purchase your rental through your account.

Summary

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.

PREFACE

(2)

LIST OF SYMBOLS

vii

1 FAMILIES OF SETS

(19)

1. Sets: general notations

(3)

2. Elementary operations on sets

(1)

3. Families of sets

(2)

4. Operations in a family of sets

(1)

5. Partitions

(1)

6. Filter bases

(3)

7. Closure operations in a set

(3)

8. (*) Lattices of sets

(3)

9. Principal limits of a family of sets

(2)

II MAPPINGS OF ONE SET INTO ANOTHER

(8)

1. Single-valued, semi-single-valued and multi-valued mappings

(2)

2. Operations on mappings

(2)

3. Upper and lower inverses of a mapping

(3)

4. Graphs

(1)

III ORDERED SETS

(17)

1. Order and equivalence

(2)

2. Countable infinite and continuum infinite sets

(2)

3. (*) Transfinite cardinal numbers

(4)

4. Ordered sets

(2)

5. (*) Transfinite ordinal numbers

(1)

6. (*) The different forms of the axiom of choice

(6)

IV TOPOLOGICAL SPACES

(37)

1. Metric spaces

(4)

2. (*) L(*)-and L(0)-spaces

(4)

3. Topological spaces

(5)

4. Sequences and filtered families

(5)

5. Separated, quasi-separated, regular and normal spaces

(3)

6. Compact sets

(5)

7. Connected sets

(3)

8. Numerical functions defined on a topological space

(3)

9. Products and sums of topological spaces

(5)

V TOPOLOGICAL PROPERTIES OF METRIC SPACES

(27)

1. Topology of a metric space

(3)

2. Sums and products of metric spaces

(2)

3. Sequences of elements

(3)

4. Totally bounded spaces and complete spaces

(3)

5. Separable sets

(1)

6. Compact sets

(2)

7. Connected sets

(3)

8. (*) Locally connected sets: curves

(4)

9. Single-valued mappings of one metric space into another

103

(7)

VI MAPPINGS FROM ONE TOPOLOGICAL SPACE INTO ANOTHER

109

(20)

1. Semi-continuous mappings

109

(4)

2. Properties of the two types of semi-continuity

113

(2)

3. Maximum theorem

115

(2)

4. Fixed points of a mapping of R into R

117

(1)

5. (*) Limits of a family of sets

118

(8)

6. (*) Hausdorff metrics

126

(3)

VII MAPPINGS OF ONE VECTOR SPACE INTO ANOTHER

129

(29)

1. Vector spaces

129

(4)

2. Linear mappings

133

(3)

3. Linear varieties, cones, convex sets

136

(8)

4. Dimension of a convex set

144

(4)

5. The gauge of a convex set

148

(6)

6. The Hahn-Banach theorem

154

(4)

VIII CONVEX SETS AND CONVEX FUNCTIONS IN THE SPACE R(n)

158

(73)

1. Topological properties of convex sets

158

(10)

2. Simplexes; Kakutani's Theorem

168

(8)

3. Matrices

176

(4)

4. Bistochastic matrices

180

(8)

5. Convex functions

188

(6)

6. Differentiable convex functions

194

(6)

7. The fundamental properties of convex functions

200

(7)

8. Quasi convex functions

207

(4)

9. The fundamental inequality of convexity

211

(4)

10. (*) Sub-XXX functions

215

(4)

11. S-convex functions

219

(7)

12. Extremal problems with convex and concave functions

226

(5)

IX TOPOLOGICAL VECTOR SPACES

231

(34)

1. Normed spaces

231

(5)

2. Topological vector spaces

236

(6)

3. General properties of convex sets

242

(3)

4. Separation by convex functions

245

(4)

5. Locally convex spaces

249

(3)

6. Banach spaces: strong convergence

252

(7)

7. Banach spaces: weak convergence

259

(6)

INDEX

265

Amazon no longer offers textbook rentals. We do!

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

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

9780486696539

0486696537

Summary

Table of Contents

Supplemental Materials

Write a Review