Preservation of closed sets under non-archimedean operators

AbstractIn recent years some characterizations of the operators which preserve closed sets, closed bounded sets and closed bounded convex sets had been given in the literature. The kinds of operators involved are semi-Fredholm and tauberian operators. In this paper we introduce non-archimedean tauberian operators and prove that they coincide with semi-Fredholm operators when the ground field is spherically complete. Also, we give some theorems of preservation of closed sets under these classes of operators