Fiber bundles and Lie algebras of top spaces

Document Type : Research Paper


Department of Mathematics, College of Sciences, Shiraz University, P.O.Box 71457-44776, Shiraz, IRAN.


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


Main Subjects