Expansiveness is very closely related to the stability theory of the dynamical systems. It is natural to consider various types of expansiveness such as countably-expansive, measure expansive, N
-expansive, and so on. In this article, we introduce the new concept of countably expansiveness for continuous dynamical systems on a compact connected smooth manifold M
by using the dense set D
, which is different from the weak expansive flows. We establish some examples having the countably expansive property, and we prove that if a vector field X
stably countably expansive then it is quasi-Anosov.
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