A Note on the Continuity of Preference Relations defined on Discrete Sets

This note discusses continuity of preference relations defined in discrete sets.Special interest is dedicated to the preference relation $\succeq$ defined in $X\equiv \cup_{n=1}^\infty\{1-1/n\}$ and such that, for each pair of points $x$ and $y$ in $X$, we have $x\succeq y$ if $|x-1/2|\geq|y-1/2|$.The relativity property of the open set concept emerges as a fundamental ingredient for this discussion and, therefore, its importance for Economic Theory is reinforced in a tranparent way.The continuity of such a relation is shown to be a particular case of a more general result: "Every correspondence with discrete domain is continuous''.