# Question about a collection of sets in the plane.

1. Sep 2, 2012

### cragar

1. The problem statement, all variables and given/known data
Show that the collection
$\{ \{a\}\times(b,c) \subset \mathbb{R^2} |a,b,c \in \mathbb{R} \}$
of vertical intervals in the plane is a basis for a topology on $\mathbb{R^2}$
3. 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.

2. Sep 2, 2012

### Dick

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. Sep 13, 2012

### nerever

Hi. Could you explain your solution a bit more? I am stuck in the same problem..