Let $X=\mathbb{R}$ and $S=[-1,1]$, i don't quite understand why $[-1,0)$ is open in $S$ but not open in $X$. As far as i know, to show a set is open, we need to show there exist an open ball $B(x,r), r> 0$ st for all $x\in [-1,0)$ ,$x\in B\subset S$, however, i still can't see why $[-1,0)$ is open in $S$ but not open in $X$. When we look at -1, i don't think this is a interior point of S.
A simple question about open set
1
$\begingroup$
general-topology
-
2But what does it mean for something to be open *in $S$* under the [subspace topology](http://en.wikipedia.org/wiki/Subspace_topology) that $S$ gains as a subset of $\mathbf R$? – 2012-06-19