Some decomposable continua and Whitney levels of their hyperspaces

We introduce the new class of continua; \(D^{**}\)-\(continua\). The classes of Wilder continua and \(D^{*}\)-continua are strictly contained in the class of \(D^{**}\)-continua. Also, the class of \(D\)-continua is bigger than the class of \(D^{**}\)-continua. Using \(D^{**}\)-continua, we give the negative answer to a Question. Furthermore, we prove that being Wilder, being \(D\), being \(D^*\) and being \(D^{**}\) are Whitney properties.