Abstract: In this paper, we discuss prolongation and
prolongational limit set. Let X be a
locally compact metric space, for a point we get some properties of the
higher positive prolongation and higher positive prolongational
limit set It is shown that if and then there is an ordinal h
such that For a set we also discuss two positive
prolongations and two positive prolongational
limit sets and get some relations among them.
We also obtain some results about the connectedness of prolongation and
prolongational limit set, and a theorem of stability. At last, we discuss
dispersive concepts and orbit space.
Keywords and phrases: prolongation, prolongational limit set, connectedness, stability, dispersiveness.
