Weakly convex sets in asymmetric normed spaces

In this work we present different results for weakly convex sets is spaces with asymmetric seminorm. We present the theorem for the well-posedness of the closest points problem and the Separation Theorem for weakly and strongly convex sets w.r.t. a quasiball. We also proved the proximal normal and Frechet normal regularities for weakly convex sets in spaces with asymmetric seminorm.