Proximaly and other topics in induced hyperspace dynamical systems arising from Alexandroff compactification

Fatemah Ayatollah Zadeh Shirazi, Behrooz Falahat, Kambiz Moghaddamfar, Bahman Taherkhani
2016 International Journal of Contemporary Mathematical Sciences  
In the following text we prove that if X is the Alexandroff compactification of a discrete space with at least two elements and f : X → X is a homeomorphism, then in the dynamical system (X, f ) the following statements are equivalent: • the dynamical system (X, f ) is proximal, Mathematics Subject Classification: 37B05, 54B20, 54H20
doi:10.12988/ijcms.2016.51046 fatcat:y4zafdv6xff7xpdj3yeritr35e