Hausdorff Dimension of Centered Sets

Abstract

In this paper we will consider nowhere dense perfect subsets of $[0,1]$ that arise as a natural generalization of symmetric perfect sets in a paper of Humke, called centered sets. These sets have relatively large basic intervals but none of the standard methods used in determining the dimension of a generalized Cantor set could be used to show that centered sets can not have zero Hausdorff dimension. The aim of this paper is to prove that and to give lower bound for this dimension..