If $G$ is compact and $K \subset G$ is closed in $G$, must $G/K$ also be compact? If $G$ is compact and $K \subset G$ is closed in $G$, must $G/K$ also be compact?
The sets $G$ is a topological group for example. 

Yes it is compact if it is endowed with the quotient topology since it is the image of the compact $G$ by the quotient map $G\rightarrow G/K$ and the image of a compact by a continue map is compact.
