Combinatorial dimension and measurements of interdependencies

The concepts of fractional Cartesian products and combinatorial dimension were originally cast in a framework of multi-dimensional lattices [1], [2], [3], [6]. In this paper, I will describe the extension of these ideas to the J — dimensional Euclidean setting RJ, taking into account its usual topological structure. As in the discrete framework of multi-dimensional lattices, the ‘combinatorial dimension’ of a set in the topological setting will be viewed as a measurement of interdependencies between coordinates of points in the given set.