in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

Not only mathematical statistics, differential equations, and models were used to analyze reduce data, but a rough set model is also employed in medical, engineering, other fields them. The goal of this paper introduce minimal structure concept produce new show that it suitable for analyzing most real-life problems, reduction attributes, decision making. We examine the effectiveness following m...