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I am reading this.

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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    Help$f$ul comme$n$t tha$n$$k$s!2010-12-31

1 Answers 1

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A Closed set is by definition a set whose complement is an open set. Note that this also includes the possibility that a set is both open and closed, for example in a space with two connected components, each component is both open and closed.

Now, in what you have highlighted the complement of the solid region (inclusive of boundary) i.e. the whole space without the region, is open. Which, means that the solid region (inclusive of boundary) is closed.

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    It makes sense now! Thanks! :)2010-12-31