  In his 1979 paper Trotman proves, using the techniques of the Thom
transversality theorem, that under some conditions on the dimensions of the
manifolds under consideration, openness of the set of maps transverse to a
stratification in the strong (Whitney) topology implies that the stratification
is $(a)$-regular. Here we first discuss the Thom transversality theorem for the
weak topology and then give a similiar kind of result for the weak topology,
under very weak hypotheses. Recently several transversality theorems have been
proved for complex manifolds and holomorphic maps. In view of these
transversality theorems we also prove a result analogous to Trotman's result in
the complex case.
