- #1

Damascus Road

- 120

- 0

a.) Show that C is a basis for a topology on R.

b.) prove that the topology generated by C is not the standard topology on R.

So, I know for C to be a basis, there must be some x [tex]\in[/tex] R,

and in the union of some C1 [tex]\bigcap[/tex] C2 there must be a C3, so that x [tex]\in [/tex] C3.

So, since my C = {[a,b), | a<b,

Letting a1 < a2 < x < b1 < b2

my C3 = [a2, b1) [tex]\in[/tex] C.

I'm confused how to work in the rational numbers however, must I truncate them or something? Don't know how this would fit into the logic..

thanks in advance.