Author | Searcรณid, Mรญcheรกl ร. author |
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Title | Elements of Abstract Analysis [electronic resource] / by Mรญcheรกl ร Searcรณid |
Imprint | London : Springer London : Imprint: Springer, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0179-6 |
Descript | XII, 300 p. 3 illus. online resource |
1. Sets -- 1.1 Set Theory -- 1.2 Relations and Functions -- 1.3 Ordered Sets -- 1.4 Ordinals -- 1.5 The Axiom of Choice -- 2. Counting -- 2.1 Counting Numbers -- 2.2 Cardinality -- 2.3 Enumeration -- 2.4 Cardinality of Unions and Products -- 3. Algebraic Structure -- 3.1 Elementary Algebraic Structures -- 3.2 Vector Spaces -- 3.3 Algebras -- 3.4 Preservation of Algebraic Structure -- 4. Analytic Structure -- 4.1 Ordered Algebraic Structure -- 4.2 Number Systems -- 4.3 Real and Complex Functions -- 4.4 Inequalities -- 5. Linear Structure -- 5.1 Linear Spaces and Algebras -- 5.2 Linear Shapes -- 5.3 Linear Functionals -- 6. Geometric Structure -- 6.1 Semimetrics and Metrics -- 6.2 Seminorms and Norms -- 6.3 Sesquilinear Forms and Inner Products -- 7. Topological Structure -- 7.1 Topologies -- 7.2 Neighbourhoods -- 7.3 Cardinality and Topology -- 7.4 Separation -- 8. Continuity and Openness -- 8.1 Preservation of Topological Structure -- 8.2 Topologies Denned by Functions -- 8.3 Derived Topological Spaces -- 8.4 Topologies on Linear Spaces -- 9. Connectedness -- 9.1 Connected Spaces -- 9.2 Pathwise Connectedness -- 10. Convergence -- 10.1 Filters -- 10.2 Limits -- 11. Compactness -- 11.1 Compact Topological Spaces -- 11.2 Compact Hausdorff Spaces -- 11.3 Local Compactness -- 12. Completeness -- 12.1 Complete Metric Spaces -- 12.2 Banach Spaces -- 12.3 Hilbert Spaces -- 12.4 Banach Algebras -- Solutions