# ans2 - Math 185. Sample Answers to Problem Set #2 Page 32...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 185. Sample Answers to Problem Set #2 Page 32 6. First suppose that S is open. Using the books definition, this means that S contains none of its boundary points. So, if z S , then z is not a boundary point of S , and it is also not an exterior point of S (if z is an exterior point of S , then it has a neighborhood that is disjoint from S , but that neighborhood contains z itself, implying z / S ). Therefore z must be an interior point of S . Conversely, if each z S is an interior point, then it is not a boundary point, so S does not contain any of its boundary points. Thus S is open. 7. a . This is just the set { 1 , i } . It is a finite set, so it has no accumulation points (see problem 10). b . All points in this set are isolated, but they tend toward the origin, so { } is the set of accumulation points. c . This is the closed first quadrant: Re z 0 , Im z 0 . d . For even values of n , this is (1 + i ) n- 1 n , with accumulation point 1 + i . For odd values of n this is- (1 +...
View Full Document

## This note was uploaded on 09/01/2010 for the course MATH 185 taught by Professor Lim during the Fall '07 term at University of California, Berkeley.

### Page1 / 3

ans2 - Math 185. Sample Answers to Problem Set #2 Page 32...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online