MATH 3220 § 1 EIGHTH HOMEWORK ASSIGNMENT Due Thursday,

A. Treibergs March 31, 2005

MATH 3220 § 1	EIGHTH HOMEWORK ASSIGNMENT	Due Thursday,
A. Treibergs		March 31, 2005

Please hand in the following exercises from the text "An Introduction to Analysis, Third Edition" by William Wade, Prentice Hall, 2004.

329 [ 3 b, 4, 5 ]

Please hand in the additional exercises.

Prove that the "topologist's sine curve" E in the plane is connected.
E = { (0,y) : -1 < y < 1} U { (x, sin(1/x)) : 0 < x < 1}
Suppose that H₁, H₂ , H₃,... is a decreasing nested sequence of nonempty compact sets of Rⁿ. Show that the intersection of all of these sets is nonempty.

The Math Department's Calculus Challenge is Saturday, April 9, 2005. Win $$$!!!

For further information, check out
http://www.math.utah.edu/ugrad/calc_challenge/.

Please hand in the following exercises from the text "An Introduction to Analysis, Third Edition" by William Wade, Prentice Hall, 2004.
329 [ 3 b, 4, 5 ]
Please hand in the additional exercises.
Prove that the "topologist's sine curve" E in the plane is connected. E = { (0,y) : -1 < y < 1} U { (x, sin(1/x)) : 0 < x < 1} Suppose that H₁, H₂ , H₃,... is a decreasing nested sequence of nonempty compact sets of Rⁿ. Show that the intersection of all of these sets is nonempty.