  This paper continues the work Glasner-Tsirelson-Weiss, ArXiv math.DS/0311450.
For a Polish group G the notions of G-continuous functions and whirly actions
are further exploited to show that: (i) A G-action is whirly iff it admits no
nontrivial spatial (= pointwise) factors. (ii) Every action of a Polish Levy
group is whirly. (iii) There exists a Polish monothetic group which is not Levy
but admits a whirly action. (iv) In the Polish group Aut(X,\mu), for the
generic automorphism T, the action of the Polish group \Lambda(T) = closure
{T^n: n \in Z} \subset Aut(X,\mu) on the Lebesgue space (X,\mu) is whirly. (v)
The Polish additive group underlying a separable Hilbert space admits both
spatial and whirly faithful actions. (vi) When G is a non-archimedean Polish
group then every G-action is spatial.
