Question about a collection of sets in the plane.

  • Thread starter cragar
  • Start date
  • #1
cragar
2,552
3

Homework Statement


Show that the collection
[itex] \{ \{a\}\times(b,c) \subset \mathbb{R^2} |a,b,c \in \mathbb{R} \} [/itex]
of vertical intervals in the plane is a basis for a topology on [itex] \mathbb{R^2} [/itex]

The Attempt at a Solution


My question is just really about (a)X(b,c)
am I just basically letting a varying across the real line and then just pairing it up
with all the points on that line. So at each vertical interval
it will be open interval going up and down from point a and starting at b and going up vertically to c.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
It's the open interval whose points all have first coordinate a and the second coordinate lies between b and c. So yes, if that's what you mean.
 
  • #3
nerever
1
0
Hi. Could you explain your solution a bit more? I am stuck in the same problem..
 

Suggested for: Question about a collection of sets in the plane.

  • Last Post
Replies
4
Views
6K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
3K
Replies
4
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
4
Views
917
Top