Topological function spaces
著者
書誌事項
Topological function spaces
（Mathematics and its applications, . Soviet ser. ; 78）
Kluwer Academic Publishers, c1992
- タイトル別名
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Topologicheskie prostranstva funkt︠s︡iĭ
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注記
Translation of: Topologicheskie prostranstva funkt︠s︡iĭ
Translated by R.A.M. Hoksbergen
Bibliography: p. 193-201
Includes index
内容説明・目次
内容説明
One service mathematics has rendered the 'Et moi, "0' si j'avait su oomment en revenir. human race. It has put common sense back je n'y serais point aile:' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'el:re of this series.
目次
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 Lindeloef 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 Lindeloef number and tightness type.- 1. Lindeloef number and tightness: the Arkhangel'skii-Pytkeev theorem.- 2. Hurewicz spaces and fan tightness.- 3. Frechet-Urysohn property, sequentiality, and the k-property of Cp(X).- 4. Hewitt-Nachbin spaces and functional tightness.- 5. Hereditary separability, spread, and hereditary Lindeloef 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 Ptak's approach.- 6. Baturov's theorem on the Lindeloef number of function spaces over compacta.- IV. Lindeloef 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 Lindeloef 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 Lindeloef number of the space Cp(X),and scattered compacta.- 8. The Lindeloef number of Cp(X) and Martin's axiom.- 9. Lindeloef ?-spaces, and properties of the spaces Cp,n(X).- 10. The Lindeloef number of a function space over a linearly ordered compactum.- 11. The cardinality of Lindeloef subspaces of function spaces over compacta.
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