  We study non-compact surfaces obtained by gluing strips
$\mathbb{R}\times(-1,1)$ with at most countably many boundary intervals along
some these intervals. Every such strip possesses a foliation by parallel lines,
which gives a foliation on the resulting surface. It is proved that the
identity path component of the group of homeomorphisms of that foliation is
contractible.

Geometric Topology;Complex Variables;General Topology