TY  - BOOK
AU  - Reisel,Robert B.
TI  - Elementary theory of metric spaces: a course in constructing mathematical proofs 
SN  - 0387907068
AV  - QA331 R45 1982
U1  - 514.32 
PY  - 1982///
CY  - New York
PB  - Springer-Verlag
KW  - Functional analysis
KW  - Functions of real variables
KW  - Metric spaces
N1  - 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
UR  - http://www.worldcat.org/title/elementary-theory-of-metric-spaces-a-course-in-constructing-mathematical-proofs/oclc/720940746&referer=brief_results
ER  -