Topological function spaces

Cover......Page 1
Title Page......Page 3
Copyright Page......Page 4
Series Editor's Preface......Page 5
Contents......Page 7
1. General questions about C_p(X)......Page 11
2. Certain notions from general topology. Terminology and notation......Page 14
3. Simplest properties of the spaces C_p(X,Y)......Page 19
4. Restriction map and duality map......Page 21
5. Canonical evaluation map of a space X in the space C_p(X)......Page 26
6. Nagata's theorem and Okunev's theorem......Page 32
1. Elementary duality theorems......Page 35
2. When is the space C_p(X)  sigma-compact?......Page 38
3. Cech completeness and the Baire property in spaces C_p(X)......Page 41
4. The Lindelof number of a space C_p(X), and Asanov's theorem......Page 43
5. Normality, collectionwise normality, paracompactness, and the extent of C_p(X)......Page 46
6. The behavior of normality under the restriction map between function spaces......Page 53
1. Lindelof number and tightness: the Arkhangel'skii-Pytkeev theorem......Page 55
2. Hurewicz spaces and fan tightness......Page 58
3. Frechet-Urysohn property, sequentiality, and the k-property of C_p(X)......Page 61
4. Hewitt-Nachbin spaces and functional tightness......Page 67
5. Hereditary separability, spread, and hereditary Lindelof number......Page 76
6. Monolithic and stable spaces in C_p duality......Page 86
7. Strong monolithicity and simplicity......Page 93
8. Discreteness is a supertopological property......Page 97
1. Tightness type properties of spaces C_p(X), where X is a compactum, and embedding in such C_p(X)......Page 101
2. Okunev's theorem on the preservation of o-compactness under t- equivalence......Page 107
3. Compact sets of functions in C_p(X). Their simplest topological properties......Page 112
4. Grothendieck's theorem and its generalizations......Page 116
5. Namioka's theorem, and Pt'ak's approach......Page 125
6. Baturov's theorem on the Lindelof number of function spaces over compacta......Page 131
1. Separating families of functions, and functionally perfect spaces......Page 135
2. Separating families of functions on compacta and the Lindelof number of C_p(X)......Page 141
3. Characterization of Corson compacta by properties of the space C_p(X)......Page 146
4. Resoluble compacta, and condensations of C_p(X) into a Sigma-product of real lines. Two characterizations of Eberlein compacta......Page 154
5. The Preiss-Simon theorem......Page 162
6. Adequate families of sets: a method for constructing Corson compacta......Page 166
7. The Lindelof number of the space C_p(X ), and scattered compacta......Page 174
8. The Lindelof number of C_p(X) and Martin's axiom......Page 178
9. Lindelof E-spaces, and properties of the spaces C_{p,n}(X)......Page 184
10. The Lindelof number of a function space over a linearly ordered compactum......Page 191
11. The cardinality of Lindelof subspaces of function spaces over compacta......Page 195
Bibliography......Page 203
Index......Page 213