On the group of homeomorphisms foliated manifolds.

The set Homeo(M) of all homeomorphisms of a manifold M onto itself is the group related to composition and inverse mapping. The group of homeomorphisms of smooth manifolds is of great importance in differential geometry and in analysis. It is known that the group Homeo(M) is a topological group in compact open topology. In this paper we investigate the group HomeoF (M) of homeomorphisms foliated manifold (M, F) with foliated compact open topology. It is proven that foliated compact open topology of the group HomeoF (M) has a countable base. It is also proven that the group HomeoF (M) is a topological group with foliated compact open topology. [ABSTRACT FROM AUTHOR]