On T0 alexandroff spaces

الملخص EN

In this paper, we study and describe some topological concepts on a special class of topological spaces called To? Alexan- dro® spaces.

We characterize the closure, the interior, and the cluster points of a subset.

We identify some of the generalized open sets as preopen, semi-open, ®?open and we study some related properties. We focus on a special important type of To? Alexandro® spaces which satisfy the ACC.

Since this is equivalent to DCC on certain ideals, we call such spaces Artinian To? Alexandro® spaces.

We get strong results for this class, such as characterization of exteremally disconnectedness.

One of the important results is ¯nding necessary and su±cient conditions for a To? Alexandro® space to be submaximal.