If 
is a fiber
bundle with 
a paracompact topological
space, then 
satisfies the homotopy lifting
property with respect to all topological spaces.
In other words, if ![g:[0,1]×X->B](/images/equations/Fibration/Inline4.svg)
is a homotopy from 
to 
,
and if 
is a lift
of the map 
with respect to 
, then 
has a lift to a map 
with respect to 
. Therefore, if you have a homotopy
of a map into 
, and if the beginning of it has a lift,
then that lift can be extended to a lift
of the homotopy itself.
A fibration is a map between topological spaces 
such that it satisfies the homotopy lifting
property.
