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**Mollier** Hi,

Rudin defines the segment $\displaystyle (a,b)$ to be the set of all real numbers $\displaystyle x$ such that $\displaystyle a<x<b$.

In one example he considers the subset $\displaystyle (a,b)$ of $\displaystyle R^2$ and says that it is not an open set if we regard it as a subset of $\displaystyle R^2$, but that it is open if we regard it as a subset of $\displaystyle R^1$.

How do I regard the segment $\displaystyle (a,b)$ as a subset of $\displaystyle R^2$? 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 $\displaystyle R^1$...

Thanks.