Working through Spivak "Calculus on Manifolds."(adsbygoogle = window.adsbygoogle || []).push({});

On p. 7, he explains that "the interior of any set A is open, and the same is true for the exterior of A, which is, in fact, the interior of R[tex]\overline{}n[/tex]-A."

Later, he says "Clearly no finite number of the open sets in [tex]O[/tex] wil cover R or, for that matter, any unbounded subset of R"

My confusion: given some interval say A = [a,b] [tex]\subset R[/tex], then R-A and (a-1,b+1) would seem to be two open sets covering R.

I clearly have misunderstood a definition.

Thanks, in advance.

Ken Cohen

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