Infinite union of closed sets that isn't closed?

  • Thread starter autre
  • Start date
  • #1
autre
117
0
So I have to find an infinite union of closed sets that isn't closed. I've thought of something that might work:

[itex]\bigcup[0,x][/itex] where [itex]0\leq x<1[/itex]. Then, [itex]\bigcup[0,x] = [0,1)[/itex], right?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
43,021
971
Yes, that is correct. 1 is not in that union because it is not in [0, x] for any x<1. If y< 1, however, there does exist x> y and y is in such [0, x]. Therefore the union contains all of [0, 1).
 
  • #3
Bacle2
Science Advisor
1,089
10
Or, you can apply DeMorgan to an intersection of opens that is not open, like (0,1/n).
 

Suggested for: Infinite union of closed sets that isn't closed?

  • Last Post
Replies
5
Views
440
  • Last Post
Replies
1
Views
316
Replies
4
Views
568
  • Last Post
Replies
6
Views
496
Replies
7
Views
2K
  • Last Post
Replies
13
Views
574
  • Last Post
Replies
22
Views
1K
  • Last Post
Replies
4
Views
1K
Replies
2
Views
451
Top