عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9780387907062
(Number (ISBN
9781461381884
NATIONAL BIBLIOGRAPHY NUMBER
Number
dltt
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Elementary Theory of Metric Spaces
General Material Designation
[Book]
Other Title Information
A Course in Constructing Mathematical Proofs /
First Statement of Responsibility
by Robert B. Reisel.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New York, NY :
Name of Publisher, Distributor, etc.
Springer New York,
Date of Publication, Distribution, etc.
1982.
SERIES
Series Title
Universitext,
ISSN of Series
0172-5939
CONTENTS NOTE
Text of Note
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.
0
SUMMARY OR ABSTRACT
Text of Note
Science 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. It is important that they understand how experiments are performed and what the results mean. In science the validity of ideas is checked by experiments. If a new idea does not work in the laboratory, it must be discarded. If it does work, it is accepted, at least tentatively. In science, therefore, laboratory experiments are the touchstones for the acceptance or rejection of results. Mathematics is different. This is not to say that experiments are not part of the subject. Numerical calculations and the examina tion of special and simplified cases are important in leading mathematicians to make conjectures, but the acceptance of a conjecture as a theorem only comes when a proof has been constructed. In other words, proofs are to mathematics as laboratory experiments are to science. Mathematics students must, therefore, learn to know what constitute valid proofs and how to construct them. How is this done? Like everything else, by doing. Mathematics students must try to prove results and then have their work criticized by experienced mathematicians. They must critically examine proofs, both correct and incorrect ones, and develop an appreciation of good style. They must, of course, start with easy proofs and build to more complicated ones.
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
9780387907062
PIECE
Title
Springer eBooks
TOPICAL NAME USED AS SUBJECT
Global analysis (Mathematics).
Mathematics.
PERSONAL NAME - PRIMARY RESPONSIBILITY
Reisel, Robert B.
CORPORATE BODY NAME - ALTERNATIVE RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Date of Transaction
20190301081200.0
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
