Some decomposable continua and Whitney levels of their hyperspaces

Abstract

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

8 pages, 1 figure