000			02254nam a22002657a 4500
999			_c58697 _d58697
005			20220105124423.0
008			220105b ||||| |||| 00| 0 eng d
020			_a9780387907062
028			_a:Variety Books Publishers & Distributors _b:B-10 Street No 2 West Vinod Nagar Delhi 110092 _c:IM2896 _d:10/12/2021
082			_a514.32 REI
100			_aReisel, Robert B
245			_aElementary theory of metric spaces _b : a course in constructing mathematical proofs _c/ Robert B Reisel
260			_aNew York _b: Springer-Verlag, _c©1982.
300			_a120 pages _c ; 24 cm
365			_b6652
505			_a 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.
520			_aScience students have to spend much of their time learning how to do laboratory work, even if they intend to become theoretical, rather than experimental, scientists. Mathematics students must try to prove results and then have their work criticized by experienced mathematicians.
650			_aMathematics
650			_aTopology
650			_aFunctions of real variables.
650			_aFunctional analysis.
650			_aMetric spaces.
700			_aReisel, Robert B
942			_cMDL