MIXED CONNECTEDNESS VIA SHADOW SPACES

Shadow spaces are quotient spaces of $A-$spaces. They provide a better understanding to the concept of $A-$spaces using their corresponding posets. In this paper, we introduce and investigate new types of Alexandroff space called upper bounded and lower bounded Alexandroff spaces. Then we study connectedness and types of mixed connectedness. we prove that an Alexandroff space X is i-j-connected iff its shadow space [X] is i-j-connected, for i,j \in {\alpha, P, S, SP,\gamma }.