We introduce the notion of topological structure, and relative to that the notions of structural topology as well as structural continuity are given. We show that for a given topological structure, structural topological spaces together with structural continuous morphisms form a concrete category. We then give the construction of the induced, coinduced, discrete and indiscrete structural topologies, proving certain results that hold for topological spaces also hold for structural topological spaces. We demonstrate that if the base category is (finitely) complete, then the category of structural topological spaces is concretely (finitely) complete. Finally we provide some illustrative examples.
