hw4 - E 1 E 2 = . 2) Suppose that E R n is connected and E...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
M421 HW 4 Due Friday Oct. 26 From Wade Section Page Number Problems 9.2 269-270 3(ab) 9.3 275-277 4, 5, 8 9.4 279 2, 3, 6 Non-book Exercises 1) For two sets A,B R n defne dist( A,B ) = in± vx A,v y B b vx vy b . (a) Show that i± E R n is closed and K R n is compact then E K = , ⇐⇒ dist( E,K ) > 0 . (b) Find two closed sets E 1 and E 2 in R 2 such that dist( E 1 ,E 2 ) = 0 but
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: E 1 E 2 = . 2) Suppose that E R n is connected and E A E . Prove that A is connected. 3) Let f be defned on R 2 by f ( x,y ) = x | y | x 2 + y 2 . For which > 0 is it true that lim ( x,y ) (0 , 0) f ( x,y ) = 0 . 1...
View Full Document

This note was uploaded on 07/25/2008 for the course MATH 421 taught by Professor Promislow during the Fall '07 term at Michigan State University.

Ask a homework question - tutors are online