Can somebody provide not open and not closed set? I even cannot imagine what does it mean. Also, I'm having a deal with such problem that there is a bounded countable set in R, and I should provide examples of sets that are: opened; closed; not opened and not closed; compact, which means bounded and closed.
[Math] Not open and not closed set
general-topology
Best Answer
Hint:
A bounded countable set in $\mathbb R$ is easy to find if you know that $\mathbb Q$ is a countable set. Can you find a bounded subset of $\mathbb Q$?
All of the other examples can be intervals in $\mathbb R$. Just play around with whether the edge points are included or not.