Closed and Bounded set We were thrown a bit of a curveball question in our first topology class, and I'm a bit puzzled by it.
The question is, is the set ${x=1}$ closed and bounded? The set is in $\mathbb{R}^{n}$.
I started with thinking that $x=1$ is a set that contains its own boundary, but don't know where else to go from here!
Thanks.
Thomas

Rely on the definition...
$S=\{1\}$ is obviously bounded
Any converging sequence of $S$ does converge in $S$ (it is constant of value $1$)
In case your question concerns a hyperplane of a multi-dimentional space :


*

*It is not bounded (I think you can come up with a divergent sequence in this hyperplane)

*Any converging sequence of this hyperplane does converge in it
