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## Homework Statement

Construct a set S in R such that

- S

- interior of S

- Closure of S

- Closure of the interior of S

- Interior of the closure of S

Are all distinct from each other.

## Homework Equations

I don't think there should be any.

## The Attempt at a Solution

I 'm pretty sure that the set has something to do with the rational numbers Q, but I'm stuck at "closure of the interior of S" and "interior of the closure of S".

So far, my attempt has been:

- S: The rational numbers Q

- int S: Empty set

- cl S: R

- cl (int S) : ???

- int (cl S) : ???

Just wondering, does this work? If not, is there a better set for this type of question?