Abstract: The concept of interior elements of subsets has been introduced in topological systems, and the related properties of interior elements have been discussed. The operator of interior elements has been defined by extent mapping and interior element mapping between a set and a frame, and the method determining topological system by the operator of interior elements has been given. The continuous mapping between topological systems is characterized by the interior elements of topological systems.

Key words: topological system, interior element, interior operator, continuous mapping