Topological Function Spaces [Paperback]

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. Nagatas theorem and Okunevs 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 Lindel?f number of a space Cp(X),and Asanovs 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 Lindel?f number and tightness type.- 1. Lindel?f number and tightness: the ArkhangelskiiPytkeev theorem.- 2. Hurewicz spaces and fan tightness.- 3. Fr?chetUrysohn property, sequentiality, and the k-property of Cp(X).- 4. HewittNachbin spaces and functional tightness.- 5. Hereditary separability, spread, and hereditary Lindel?f 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. Okunevs theorem on the preservation of Q-compactness under t-equivalence.- 3. Compact sets of functions in Cp(X). Their simplest topological properties.- 4. Grothendiecks theorem and its generalizations.- 5. Namiokas theorem, and Pt?ks approach.- 6. Baturovs theorem on the Lindel?f number of function spaces over compacta.- IV. Lindel?f number type properties for function spaces over compacta similar to Eberlein compacta, and properties of such compacta.- 1. Separating families of l“)