# Does closed set contain only boundary points or interior points also?

It says

Intuitively, an open set is a solid region minus its boundary. If we include the boundary, we get a closed set, which formally is defined as the complement of an open set.

Now, question is if a closed set includes interior points also then how can it be complement?

I know basic set theory. Enlighten me! :)

Thanks!

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The closed set you get by including the boundary is not the complement of the previously mentioned open set. It is the complement of a different open set, namely the "outside" of the solid region. –  Rahul Dec 31 '10 at 7:09
Helpful comment thanks! –  Pratik Deoghare Dec 31 '10 at 7:20