E. Dyer [2] proved that there is no continuous decomposition of a compact irreducible continuum into decomposable continua which is an arc with respect to its elements. The author extends Dyer's result to the plane. Consider a continuous decomposition of the plane into nonseparating compact continua. R. L. Moore [6] has shown that the decomposition space is homeomorphic to the plane. Using Moor...

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.