Approximate inverse limits and (m,n)-dimensions

Abstract

In 2012, V. Fedorchuk, using m-pairs and n-partitions, introduced the notion of the (m, n)-dimension of a space. It generalizes covering dimension. Here we are going to look at this concept in the setting of approximate inverse systems of compact metric spaces. We give a characterization of (m,n)-dimX, where X is the limit of an approximate inverse system, strictly in terms of the given system.