SEMITOPOLOGICAL MODULES

Abstract

Given a topological ring R, we study semitopological R-modules, construct their completions, Bohr and borno modications. For every topological space X, we construct the free (semi)topological R-module over X and prove that for a k-space X its free semitopological R-module is a topological R-module. Also we construct a Tychono space X whose free semitopological R-module is not a topological R-module.