A Cp-Theory Problem Book: Topological and Function Spaces

Detailed summary of exercise sectionsPreface Introduction 1.1. Basic notions of topology and function spaces1.1.1. Topologies, axioms of separation and a glance at Cp(X) 1.1.2. Products, cardinal functions and convergence 1.1.3. Metrizability and completeness1.1.4. Compactness type properties in function spaces 1.1.5. More on completeness. Realcompact spaces Bibliographic notes 1.2. Solutions of problems 1.001-1.500 1.3. Bonus results: some hidden statements1.3.1. Standard spaces 1.3.2. Metrizable spaces and compact spaces1.3.3. Properties of continuous maps1.3.4. Covering properties, normality and open families1.3.5. Product spaces and cardinal invariants1.3.6. Raznoie (unclassified results)1.4. Open problems 1.4.1. Local properties 1.4.2. Discreteness of X and completeness of Cp(X)1.4.3. Dense subspaces 1.4.4. The Lindelöf property in X and Cp(X) 1.4.5. Other covering properties 1.4.6. Mappings which involve Cp-spaces 1.4.7. Very general questions 1.4.8. Fuzzy questions1.4.9. Naïve questions 1.4.10. Raznoie (unclassified questions)1.5. Bibliography1.6. List of special symbols1.7. Index