The orbit spaces of linearly ordered systems on continuums

In this paper, the concept of an orbit space is generalized from a discrete dynamical system (X, f) to a linearly ordered system {Xα,πβ , Γ}, and it is shown that a general orbit space is a continuum if each Xα is a continuum in a linearly ordered system {Xα, πβ, Γ}. As a special case, it is obtained that the orbit space of any discrete dynamical system (X, f) is a continuum if X is a continuum.