A conglomerate of exponential supercategories of the category of finitely generated topological spaces

Summary For every ordinaln > 1 we define a categoryT_n of topological spaces in ech's sense which is isomorphic to a category ofn-ary monorelational systems. We show that every categoryT_n is an exponential supercategory of the categoryB of finitely generated topological spaces, which means that well-behaved function spacesG^H can be defined inT_n wheneverG B.