Journal of Applied Mathematics & Bioinformatics

The orbit spaces of linearly ordered systems on continuums

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• Abstract

  In this paper, the concept of an orbit space is generalized from a discrete dynamical system (X, f) to a linearly ordered system {X_α,π^β , Γ}, and it is shown that a general orbit space is a continuum if each X_α is a continuum in a linearly ordered system  {X_α, π^β, 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.