  In this work, we investigate diffeomorphisms whose positiveness of
topological entropy is destroyed by singular suspensions. We show that this
phenomenon is rare in the set of $C^1$-diffeomorphisms. Precisely, we prove
that for an open and dense set of $C^1$-diffeomorphism positive topological
entropy is preserved by singular suspensions, even for suspensions with
infinitely many singularities. We prove a similar result to the conservative
diffeomorphisms. We apply our techniques to show that every expansive singular
suspension $C^{1+\epsilon}$-flow over a three-dimensional manifold has positive
topological entropy. Finally, we explore this phenomenon for Anosov dynamics,
showing that to nullify the topological entropy for Anosov suspension flow, the
set of singularities must capture the non-wandering set.
