Topological Function Spaces
Language: English
Published by Springer, Springer Okt 2012, 2012
- Softcover
- New
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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 216 pp. Englisch.…
Seller Inventory # 9789401051477
- Title
- Topological Function Spaces
- Author
- A. V. Arkhangel'skii
- Publisher
- Springer, Springer Okt 2012
- Publication year
- 2012
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 940105147X
- ISBN 13
- 9789401051477
- Item weight
- 335 grams
- Dimensions
- 235x155x12 mm
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