  Let $M$ be a smooth connected orientable closed surface and $f_0\in
C^\infty(M)$ a function having only critical points of the $A_\mu$-types,
$\mu\in\mathbb N$. Let ${\mathcal F}={\mathcal F}(f_0)$ be the set of functions
$f\in C^\infty(M)$ having the same types of local singularities as those of
$f_0$. We describe the homotopy type of the space $\mathcal F$, endowed with
the $C^\infty$-topology, and its decomposition into orbits of the action of the
group of "left-right changings of coordinates".
