Existence of differentiable connections on top spaces

Document Type : Regular Paper


Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran


In this paper, differentiable connections on top spaces are studied and some conditions on which there is no
differentiable connection passing from a given point in the top space are found. In a special case, the Euclidean
space 􀔹􀬶 is considered as a top space and the existence of differentiable connections is studied. Finally, we prove that the smoothness condition of the inverse map in the definition of a top space is redundant.