In this paper, we investigate some properties on a class of T0 A−spaces called upper bounded. This class contains properly the class of Artinian T0 A−spaces. We prove that if X is a UB T0 A−space, then it is always strongly irresolvable and ∀x ∈ X, ˆ x ∅. Moreover, we prove that = PO(X) ⊆ SO(X). We present necessarily and sufficient conditions for a UB T0 A−space to be submaximal, hypeconnected, and extremally disconnected. In addition, the relationship between UB and other types of T0 A−spaces are discussed with some examples.