Inhaltsangabe

0. General information on Cp(X) as an object of topological algebra. Introductory material.- 1. General questions about Cp(X).- 2. Certain notions from general topology. Terminology and notation.- 3. Simplest properties of the spaces Cp(X, Y).- 4. Restriction map and duality map.- 5. Canonical evaluation map of a space X in the space CpCp(X).- 6. Nagata s theorem and Okunev s theorem.- I. Topological properties of Cp(X) and simplest duality theo-rems.- 1. Elementary duality theorems.- 2. When is the space Cp(X) u-compact?.- 3. tech completeness and the Baire property in spaces Cp(X).- 4. The Lindelöf number of a space Cp(X),and Asanov s theorem.- 5. Normality, collectionwise normality, paracompactness, and the extent of Cp(X).- 6. The behavior of normality under the restriction map between function spaces.- II. Duality between invariants of Lindelöf number and tightness type.- 1. Lindelöf number and tightness: the Arkhangel skii Pytkeev theorem.- 2. Hurewicz spaces and fan tightness.- 3. Fréchet Urysohn property, sequentiality, and the k-property of Cp(X).- 4. Hewitt Nachbin spaces and functional tightness.- 5. Hereditary separability, spread, and hereditary Lindelöf number.- 6. Monolithic and stable spaces in Cp-duality.- 7. Strong monolithicity and simplicity.- 8. Discreteness is a supertopological property.- III. Topological properties of function spaces over arbitrary compacta.- 1. Tightness type properties of spaces Cp(X), where X is a compactum, and embedding in such Cp(X).- 2. Okunev s theorem on the preservation of Q-compactness under t-equivalence.- 3. Compact sets of functions in Cp(X). Their simplest topological properties.- 4. Grothendieck s theorem and its generalizations.- 5. Namioka s theorem, and Pták s approach.- 6. Baturov s theorem on the Lindelöf number of function spaces over compacta.- IV. Lindelöf number type properties for function spaces over compacta similar to Eberlein compacta, and properties of such compacta.- 1. Separating families of functions, and functionally perfect spaces.- 2. Separating families of functions on compacta and the Lindelöf number of Cp(X).- 3. Characterization of Corson compacta by properties of the space Cp(X).- 4. Resoluble compacta, and condensations of Cp(X) into a ? -product of real lines. Two characterizations of Eberlein compacta.- 5. The Preiss Simon theorem.- 6. Adequate families of sets: a method for constructing Corson compacta.- 7. The Lindelöf number of the space Cp(X),and scattered compacta.- 8. The Lindelöf number of Cp(X) and Martin s axiom.- 9. Lindelöf ?-spaces, and properties of the spaces Cp, n(X).- 10. The Lindelöf number of a function space over a linearly ordered compactum.- 11. The cardinality of Lindelöf subspaces of function spaces over compacta.

Klappentext

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