Revealed preference axioms for rational choice on nonfinite sets

Following the work of Bandyopadhyay and Sengupta, we analyze the rationalization of a choice function in terms of the revealed preference but in a more general context: choice sets with a continuum of alternatives. Firstly it is proved that some results which are verified in the finite case are not true in this context and new conditions to characterize the different kinds of rationality are stated. Furthermore, we analyze the continuity of the revealed preference and a characterization of open revealed preferences in terms of the hemicontinuity of the choice function is obtained.