A note on continuity properties of relations

This note provides 4 equivalent conditions with the continuity of relations adopted by Brattka and Hertling to investigate computability of relations. As the case of continuous functions, each condition characterlises continuous relations by respectively using open sets, neighbourhoods, closures, and closed sets. A notion of sequential continuity is also studied. We show a relevance between continuous relations and sequentially continuous relations which is, again, analogous to the case of functions.