Some Results on the Minkowski Difference in Topological Vector Spaces

This work highlights important topological properties of Minkowski operations defined in topological vector spaces. The distributivity of Minkowski sum and difference operations with respect to the Cartesian product of sets is proved. Conditions under which the density property of sets is preserved under Minkowski operations are obtained. Furthermore, it is established as a theorem that the Minkowski difference operation is continuous in the class of compact convex sets, and this is proved using topological methods.