For the final week of my proof-writing class, my professor decided to dabble in topology since that is her favorite topic in math. However, I am having a bit of trouble understanding one of the homework questions we were given.
For the following subspace of $\mathbb{R}^n$, determine the interior points, whether or not the set is open, and whether or not the set is connected:
$\mathbb{R}^3$- {$0$}
I am having trouble envisioning what this subspace is exactly. I believe that once I understand the space I should be able to answer the questions. Is this a trick question, where $\mathbb{R}^3$- {$0$} is the same thing as saying $\mathbb{R}^3$? Or does this mean that any point we select in $\mathbb{R}^3$ cannot contain a zero, meaning we exclude the $xy$, $xz$ and $yz$ planes? These are just some ideas I have come up with... any insight would be greatly appreciated.