In this talk, we present the concepts of expansive homeomorphisms in the context of quasi-uniform spaces. We continue with our analysis on expansive homeomorphisms by extending the results from quasi-metric spaces to quasi-uniform spaces. It turns out that an expansive homeomorphism on a quasi-uniform space is also an expansive homeomorphism on its induced quasi-uniformity but the converse does not hold in general. We show that if a homeomorphism on a quasi-uniform space is expansive then the quasi-uniform space is always a Kolmogorov space. Moreover, we generalize the concept of expansive measures in the sense of Morales and Sirvent to quasi-uniform spaces point of views.

Joint work with S.M. Zweni