Math 554 Homework Assignments

MATH 554 - Math 703 I
Analysis I

Homework and Sample Problems
(Each Problem is worth 10 pts.)

No. Assignment Due Page and No.'s Solutions

#2
Tuesday (9/9)
See Page 3 of Lecture Set #1.

#3
Wednesday (10/8)
(Tues for 10 pts extra credit) All problems assume that the set E is a subset of a metric space (X,d).

The following problems only require what was covered through Thursday's lecture:

Show that each neighborhood in IR^k is convex (check text for definition).
Prove that E' is closed.
Prove that the derived sets of E and of the closure of E coincide.
Do E and E' have the same set of limit points?
Prove that the closure of E is a closed set.

Additional problems.
Page 43 of text: #5, #10, and #11 (for metrics d_2 and d_5) HW #3

#4
Thursday (10/23)
Click here
EC/Grad Problem: Show IR is complete. HW #4
EC/Grad Soln

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated Nov. 2, 2003.
This page ©2003-2004, The Board of Trustees of the University of South Carolina.
URL: http://www.,math.sc.edu/~sharpley/math554

Return to Math 554 Home Page

No.	Assignment Due	Page and No.'s	Solutions
#2	Tuesday (9/9)	See Page 3 of Lecture Set #1.
#3	Wednesday (10/8) (Tues for 10 pts extra credit)	All problems assume that the set E is a subset of a metric space (X,d). The following problems only require what was covered through Thursday's lecture: Show that each neighborhood in IR^k is convex (check text for definition). Prove that E' is closed. Prove that the derived sets of E and of the closure of E coincide. Do E and E' have the same set of limit points? Prove that the closure of E is a closed set. Additional problems. Page 43 of text: #5, #10, and #11 (for metrics d_2 and d_5)	HW #3
#4	Thursday (10/23)	Click here EC/Grad Problem: Show IR is complete.	HW #4 EC/Grad Soln



This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated Nov. 2, 2003. This page ©2003-2004, The Board of Trustees of the University of South Carolina. URL: http://www.,math.sc.edu/~sharpley/math554