Abstract
This chapter provides an overview of dimension theory. It presents the concept of dimension of a topological space (X, T). As dimension theory is a branch of topology and a vast topic, the chapter discusses only the most basic and most important issues. It focuses on topological, metric, and measure-theoretic and probabilistic dimensions. A topological space (X, T) satisfies the separation axiom T1 if two distinct points in X have neighborhoods that do not contain the other point. The chapter also presents an example of a metric dimension, namely, the Hausdorff dimension. Hausdorff dimension can be defined in a more general setting and in more general terms. The chapter also discusses other metric dimensions related to Hausdorff dimension. It also shows the calculation of the Hausdorff and box dimension of self-affine fractal sets generated by ordinary and recurrent iterated function systems (IFSs).
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