Suppose $G$ is a topological group and $H\leq G$ a normal/closed subgroup of $G$. If $H$ is contractible, does the quotient map $p: G\rightarrow G/H$ form a fibre bundle?
Is there a more general condition on $G$ or $H$ that guarantees that the map $p: G\rightarrow G/H$ is a fibre bundle? References for both of these questions will be warmly received