I am studying The Transversality Theorem introduced in Sect. 2.3 of the book "Differential Topology" by Guillemin, V and Pollack, A. It seems that the manifolds and submanifolds considered there are all assumed to be smooth, so I am curious if the smoothness assumption can be relaxed.
More precisely, I was wondering: whether this theorem would hold also for C^r (r\ge 1) manifolds? Are there any references about this?
Thanks.