On the Kuratowski Limit Operators1

In the paper we give formal descriptions of the two Kuratowski limit oprators: Li S and Ls S, where S is an arbitrary sequence of subsets of a fixed topological space. In the two last sections we prove basic properties of these lower and upper topological limits, which may be found e.g. in [19]. In the sections 2–4, we present three operators which are associated in some sense with the above mentioned, that is lim inf F , lim sup F , and limes F , where F is a sequence of subsets of a fixed 1-sorted structure.