On limit stability of special classes of continuous maps

Biquotient, effective descent, triquotient, open and proper maps were described in forthcoming paper in [M.M. Clementino, D. Hofmann, Proc. Amer. Math. Soc., to be published] by their lifting properties of chains of convergent ultrafilters. In this paper we use these characterizations to prove their stability under special limits. By their similar behaviour on lifting chains of convergent ultrafilters, on one hand we obtain several results on limit stability of open and perfect maps, and, on the other hand we give unified proofs of the pullback stability and of the product stability of biquotient, effective descent and triquotient maps.