Let $(M,g)$ be a closed Riemannian manifold, if $Scal^g>0$, we know that in a metric space of $M$, there is a neighborhood of $g$, such that all metrics in this neighborhood have the positive scalar curvature. In other words, we can choose a generic metric with P.S.C.-property.

**Q** If we replace the PSC with Non-negative scalar curvature, can we get a similar property? Is there any/some research about such a question?