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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

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    By *fiber bundle* you mean *locally trivial fiber bundle*?2011-10-18
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    @Mariano Yes I mean it is locally trivial. Could you provide me with an example of one that is not? I guess I always thought this was one of the defining characteristics of a fiber bundle.2011-10-18
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    @mjones - perhaps [this](http://mathoverflow.net/questions/57015/which-principlal-bundles-are-locally-trivial) MO question will help?2011-10-18

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