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**VonNemo19** I'm supposed to determine whether the following sets (all subsets of $\mathbb{R}^2$) are closed, open, perfect, and /or bounded.

A finite set.

This is strange. Isn't any neighborhood finite? Those are open. Is the book saying any finite subset of $\mathbb{R}^2$ is closed. The set of all integers.

Am I wrong to say that this set has no limit points? What does it look like in $\mathbb{R}^2$? All the points $(x,y)$ in the plane where $x,y\in\mathbb{Z}$ ?

The set consisting of the numbers $\frac{1}{n},~~(n=1,2,3,...)$.

The set of complex numbers.

The segment $(a,b)$.

I thought I had this before these examples. If maybe you could justify one of these for me it would help.