On upper bounded T_0 Alexandroff spaces

摘要

In this paper, we investigate some properties on a class of T0 A.spacescalled upper bounded. This class contains properly the class of ArtinianT0 A.spaces. We prove that if X is a UB T0 A.space, then it is alwaysstrongly irresolvable and 佂x 伕 X, .x .= .. Moreover, we provethat = PO(X) 伜 SO(X). We present necessarily and sufficient conditionsfor a UB T0 A.space to be submaximal, hypeconnected, andextremally disconnected. In addition, the relationship between UB andother types of T0 A.spaces are discussed with some examples.