  We answer positively a question of Ryzhikov, namely we show that being a
relatively weakly mixing extension is a comeager property in the Polish group
of measure preserving transformations. We study some related classes of ergodic
transformations and their interrelations. In the second part of the paper we
show that for a fixed ergodic T with property A, a generic extension $\hat{T}$
of T also has the property A. Here A stands for each of the following
properties: (i) having the same entropy as T, (ii) Bernoulli, (iii) K, and (iv)
loosely Bernoulli.
