New dimension-theory techniques for constructing infinite-dimensional examples

Abstract

Dimension theory for separable metric spaces is approached using the concept of essential families (for example, the n pairs of opposite faces of the n-cube). A new theory of essential families is developed and is used to construct examples of infinite-dimensional compacta that contain no closed n-dimensional (n ⩾ 1) subsets; these constructions are conceptually much easier than previous ones. Also, the theory is used to construct easy examples of n-dimensional, totally disconnected spaces.