General construction of monoidal closed structures in topological, uniform and nearness spaces

Abstract

/Introduction: In the following paper we consider topological structures on function spaces and cartesian products being connected by an exponential law of the form C(XeY,Z) ~ C(X,C(Y,Z)). Topological categories provided with such a "monoidal closed" structure are suitable base categories for topological algebra, algebraic topology, automata-or duality theory, in particular if ~ is symmetric or the usual direct product. We start from a purely categorical point of view proving an extension theorem which later turns out to be very convenient for the construction of monoidal closed structures in concrete categories, namely in topological spaces, uniform spaces, merotopic spaces and nearness spaces.