  We introduce the notion of ST-pairs of triangulated subcategories, a
prototypical example of which is the pair of the bound homotopy category and
the bound derived category of a finite-dimensional algebra. For an ST-pair
$(\C,\D)$, we construct an order-preserving map from silting objects in $\C$ to
bounded $t$-structures on $\D$ and show that the map is bijective if and only
if $\C$ is silting-discrete if and only if $\D$ is $t$-discrete. Based on a
work of Qiu and Woolf, the above result is applied to show that if $\C$ is
silting-discrete then the stability space of $\D$ is contractible. This is used
to obtain the contractibility of the stability spaces of some Calabi--Yau
triangulated categories associated to Dynkin quivers.
