I have to show that
is a topology. I know that this is not a topology, because it forms the basis for a topology on . But why is this the case? I am thinking of the case, for instance, . I don't think this is in , or am I incorrect?
Thanks in advance,
Also, can I form the whole of the real line if I changed that to ?
In the case of the set above, it's easy enough to see that any finite intersection of half-open intervals is again a half-open interval. So is the base for a topology (the half-open interval topology).