  This paper is devoted to the study of the topological pressure dimension for
almost additive sequences, which is an extension of topological entropy
dimension. We investigate fundamental properties of the topological pressure
dimension for almost additive sequences. In particular, we study the
relationships among different types of topological pressure dimension and
identifies an inequality relating them. Also, we show that the topological
pressure dimension is always equal to or greater than 1 for certain special
almost additive sequence.
