Small inductive dimension and Alexandroff topological spaces

Alexandroff spaces include finite spaces and have a wide range of applications in many areas such as computer graphics and image analysis. We give results on small inductive dimension of Alexandroff T0-spaces. Particularly, we characterize the small inductive dimension through connected tuples and study standard properties of Dimension Theory using this characterization. Also, we investigate the relations between the small inductive dimension, the large inductive dimension, and the covering dimension in the class of all Alexandroff T0-spaces. We finally put questions on dimension of Alexandroff T0-spaces.