Real Analysis Textbook Metric Spaces
Please solve the problems in B.pdf file by using the textbook.
The topics covered in this problem set are:
1. Metric spaces. Basic concepts ( Sections 5.1-5.2 )
Problems: - Section 5--# 1,2,4,5,6,7
2. Convergence. Open and closed sets (Sections 6.1-6.6)
Problems: - Section 6--# 1,2,3,4,5,9,10
3. Complete metric spaces (Sections 7.1-7.4)
Problems: - Section 7--# 1,3,4,5,7,9
4. Contraction mappings (Sections 8.1-8.3)
Problems: - Section 8 --# 1,2,4,6
5. Topological spaces
a. Basic Concepts (Sections 9.1,9.3,9.5.9.6)
Problems: - Section 9 --# 1,2,5
b. Compactness (Sections 10.1-10.3)
c. Compactness in Metric spaces (Sections 11.1-11.4)
Problems: - Section 11 --# 1,2,3,4
d. Real functions on Metric and Topological Spaces(Sections 12.1.12.2)
Problems: - Section 12 --# 1,2,3,5,6
6. Linear spaces
a. Basic Concepts (Sections 13..1-13.6)
Problems: - Section 13 --# 1,2,3,5,6
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Attachments
Solution Summary
A real analysis for textbook metric spaces is examined.
Metric space real analysis
From Contraction Mapping.
The link to my textbook:
http://books.google.com/books?id=z8IaHgZ9PwQC&pg=PA72&dq=unique+solution+contraction+mapping&lr=#PPA66,M1
Section 8:Contraction Mapping from page 66 to page 77.
Please solve for #5 and #6 based on our reference.
If you have any question or suggestion, please contact me. Thank you.