Title | General Topology II [electronic resource] : Compactness, Homologies of General Spaces / edited by A. V. Arhangel'skii |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1996 |
Connect to | http://dx.doi.org/10.1007/978-3-642-77030-2 |
Descript | VII, 256 p. online resource |
ยง1. Compactness and Its Different Forms: Separation Axioms -- 1.1. Different Definitions of Compactness -- 1.2. Relative Compactness -- 1.3. Countable Compactness -- 1.4. Relative Countable Compactness -- 1.5. Pseudocompact Spaces -- 1.6. Separation Axioms and Properties Related to Compactness -- 1.7. Star Characterizations of Countable Compactness and Pseudocompactness -- ยง2. Compactness and Products -- 2.1. Tikhonov's Theorem on Compactness of the Product -- 2.2. Products of Countably Compact Spaces -- 2.3. Products of Pseudocompact Spaces -- 2.4. Total Countable Compactness and Total Pseudocompactness -- 2.5. Compactness with Respect to a Fixed Ultrafilter (?-Compactness) -- 2.6. ?-Products of Compact Spaces -- ยง3. Continuous Mappings of Compact Spaces -- 3.1. Theorem on Compactness of the Image and Its Consequences -- 3.2. Continuous Images of โStandardโ Compacta -- 3.3. Open Mappings of Compacta and Dimension -- 3.4. Mardeลกi?'s Factorization Theorem -- 3.5. Continuous Images of Ordered Compacta -- 3.6. Pseudocompactness and Continuous Mappings -- 3.7. Continuous Mappings and Extremally Disconnected Compacta -- 3.8. Scattered Compacta and Their Images -- ยง4. Metrizability Conditions for Compact, Countably Compact and Pseudocompact Spaces -- 4.1. Classical Results and the Theorem of Chaber -- 4.2. Theorems of Dow and Tkachenko -- 4.3. Point-countable and ?-Point-finite Bases -- 4.4. Quasi-developments and ??-Bases -- 4.5. Strongly N0-Noetherian Bases -- 4.6. Rank of a Base and Metrizability Conditions for Compacta -- 4.7. Symmetrics and Metrizability of Compacta -- ยง5. Cardinal Invariants in the Class of Compacta -- 5.1. Network Weight, Diagonal Number and Weight of Compacta -- 5.2. Pseudocharacter and Character in the Class of Compacta -- 5.3. First Countable Compacta -- 5.4. Perfectly Normal Compacta -- 5.5. Continuous Images of First Countable Compacta -- 5.6. Sequential Compacta and the First Axiom of Countability Almost Everywhere -- 5.7. Corson Compact Spaces and N0-Monolithicity -- 5.8. Compacta of Countable Tightness -- 5.9. Mappings of Compacta onto Tikhonov Cubes I? -- 5.10. Dyadic Compacta -- 5.11. Supercompacta and Extensions of the Class of Dyadic Compacta -- ยง6. Compact Extensions -- 6.1. General Remarks about Compact Extensions -- 6.2. Compact T1-Extensions -- 6.3. Embedding Topological Spaces into Compact T1-Spaces of Countable Weight -- 6.4. Compact Hausdorff Extensions, Relation of Subordination -- 6.5. Compact Extensions of Locally Compact Hausdorff Spaces -- 6.6. Duality Between Properties of a Space and of Its Remainder -- 6.7. Compact Extensions and Cardinal Invariants -- 6.8. Compact Hausdorff Extensions and Perfect Mappings -- 6.9. Properties of the ?ech-Stone Extension -- 6.10. Closing Remarks Concerning Compact Hausdorff Extensions -- ยง7. Compactness and Spaces of Functions -- 7.1. Natural Topologies on Spaces of Functions -- 7.2. Joint Continuity and Compact-Open Topology -- 7.3. Stone-Weierstrass Theorem -- 7.4. Convex Compact Sets and Krein-Milman Theorem -- 7.5. Theorem of Alaoglu and Convex Hulls of Compacta -- 7.6. Fixed-Point Theorems for Continuous Mappings of Convex Compacta -- 7.7. Milyutin Compact Spaces -- 7.8. Dugundji Compact Spaces -- ยง8. Algebraic Structures and Compactness โ A Review of the Most Important Results -- 8.1. Compacta and Ideals in Rings of Functions -- 8.2. Spectrum of a Ring. Zariski Topology -- 8.3. The Space of Maximal Ideals of a Commutative Banach Algebra -- 8.4. The Stone Space of a Boolean Algebra -- 8.5. Pontryagin's Duality Theory -- 8.6. Compact Extensions of Topological Groups. Almost Periodic Functions -- 8.7. Compacta and Namioka's Theorem About Joint Continuity of Separately Continuous Functions -- 8.8. Fragmentable and Strongly Fragmentable Compacta and Radon-Nikodรฝm Compact Spaces -- 8.9. Hilbert Modules over C*-Algebras of Continuous Functions on Compacta -- 8.10. Compact Subsets of Topological Fields -- 8.11. Locally Compact Topological Groups and Paracompactness -- 8.12. Final Remarks -- References