  In this article we study some interesting properties of the $q$-Analog
singular homology, which is a generalization of the usual singular homology,
suitably adapted to the context of $N$-complex and amplitude homology
\cite{kapranov}. We calculate the $q$-Analog singular homology of a convex
space. Although it is a local matter; this is an important step in order to
understand the presheaf of $q$-chains and its algebraic properties. Our result
is consistent with those of Dubois-Viol\`ette & Henneaux \cite{dubois3}. Some
of these results were presented for the XVIII Congreso Colombiano de
Matem\'aticas in Bucaramanga, 2011.
