  A poset-stratified space is a pair $(S, S \xrightarrow \pi P)$ of a
topological space $S$ and a continuous map $\pi: S \to P$ with a poset $P$
considered as a topological space with its associated Alexandroff topology. In
this paper we show that one can impose such a poset-stratified space structure
on the homotopy set $[X, Y]$ of homotopy classes of continuous maps by
considering a canonical but non-trivial order (preorder) on it, namely we can
capture the homotopy set $[X, Y]$ as an object of the category of
poset-stratified spaces. The order we consider is related to the notion of
\emph{dependence of maps} (by Karol Borsuk). Furthermore via homology and
cohomology the homotopy set $[X,Y]$ can have other poset-stratified space
structures. In the cohomology case, we get some results which are equivalent to
the notion of \emph{dependence of cohomology classes} (by Ren\'e Thom) and we
can show that the set of isomorphism classes of complex vector bundles can be
captured as a poset-stratified space via the poset of the subrings consisting
of all the characteristic classes. We also show that some invariants such as
Gottlieb groups and Lusternik--Schnirelmann category of a map give
poset-stratified space structures to the homotopy set $[X,Y]$
