Open and closed functions

  • Thread starter StatusX
  • Start date
  • #1
StatusX
Homework Helper
2,564
1

Main Question or Discussion Point

I'm trying to understand open and closed functions, and right now I'm on the projection from R^2 to R, with f(x,y)=x. It seems this is both open and closed, but the wikipedia article on open and closed functions seems to disagree:

(Note that product projections need not be closed. Consider for instance the projection p1 : R2 → R on the first component; A = {(x,1/x) : x≠0} is closed in R2, but p1(A) = R-{0} is not closed.)
I don't understand what exactly A is, and I can't think of any counterexamples myself. Are they talking about the same function as me? Can someone explain any of this?
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
In their example, A is the hyperbola given by the equation xy = 1.
 
  • #3
StatusX
Homework Helper
2,564
1
I see. So it's not closed. Thanks.
 

Related Threads for: Open and closed functions

  • Last Post
Replies
10
Views
3K
Replies
7
Views
1K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
10
Views
9K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
3K
Replies
2
Views
2K
Top