On the Quantization Dimension of Maximal Linked Systems

Abstract

We prove that for a compact metric space \( X \) and for a nonnegative real \( b \) not exceeding the lower box dimension of \( X \), there exists a maximal linked system in \( \lambda X \) with lower quantization dimension \( b \) and support \( X \). There also exists a maximal linked system in \( \lambda X \) with support \( X \) whose lower and upper quantization dimensions coincide respectively with the lower and upper box dimensions of \( X \).