Hi,

Rudin defines the segment to be the set of all real numbers such that .

In one example he considers the subset of and says that it is not an open set if we regard it as a subset of , but that it is open if we regard it as a subset of .

How do I regard the segment as a subset of ? The way I see it from his definition of a segment, it is just a part of the "x-axis" and would be open just as in ...

Thanks.