Elementary theory of metric spaces : a course in constructing mathematical proofs / Robert B. Reisel
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TextLanguage: English Publication details: New York : Springer-Verlag, c1982. Description: 120 p ; 24 cmISBN: 0387907068; 9783540907060Subject(s): Functional analysis | Functions of real variables | Metric spacesDDC classification: 514.32 LOC classification: QA331 | R45 1982Online resources: WorldCat details | Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | Item holds |
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EWU Library Reserve Section | Non-fiction | 514 REE 1982 (Browse shelf(Opens below)) | C-1 | Not For Loan | 878 |
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| 512 HET 2002 Topics in algebra / | 512 HET 2002 Topics in algebra / | 512 LAL 1996 Linear algebra and its applications / | 514 REE 1982 Elementary theory of metric spaces : | 515 ALM Mathematical analysis for economists. | 515.15 ANC 1995 Calculus with analytic geometry / | 515.15 ANC 1999 Calculus : |
Includes index
TOC 0. Some Ideas of Logic.- I. Sets and Mappings.- 1. Some Concepts of Set Theory.- 2. Some Further Operations on Sets.- 3. Mappings.- 4. Surjective and Injective Mappings.- 5. Bijective Mappings and Inverses.- II. Metric Spaces.- 1. Definition of Metric Space and Some Examples.- 2. Closed and Open Balls; Spheres.- 3. Open Sets.- 4. Closed Sets.- 5. Closure of a Set.- 6. Diameter of a Set; Bounded Sets.- 7. Subspaces of a Metric Space.- 8. Interior of a Set.- 9. Boundary of a Set.- 10. Dense Sets.- 11. Afterword.- III. Mappings of Metric Spaces.- 1. Continuous Mappings.- 2. Continuous Mappings and Subspaces.- 3. Uniform Continuity.- IV. Sequences in Metric Spaces.- 1. Sequences.- 2. Sequences in Metric Spaces.- 3. Cluster Points of a Sequence.- 4. Cauchy Sequences.- 5. Complete Metric Spaces.- V. Connectedness.- 1. Connected Spaces and Sets.- 2. Connected Sets in R.- 3. Mappings of Connected Spaces and Sets.- VI. Compactness.- 1. Compact Spaces and Sets.- 2. Mappings of Compact Spaces.- 3. Sequential Compactness.- 4. Compact Subsets of R.- Afterword.- Appendix M. Mathematical Induction.- Appendix S. Solutions.
AS
Tahur Ahmed
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