Fiber bundles and Lie algebras of top spaces

Abstract

In this paper, by using of Frobenius theorem a relation <br />between Lie subalgebras of the Lie algebra of a top space T and Lie <br />subgroups of T(as a Lie group) is determined. As a result we <br />can consider these spaces by their Lie algebras. We show that a top <br />space with the finite number of identity elements is a C^{∞} principal <br />fiber bundle, by this method we can characterize top spaces.