Continuity and equity with infinite horizons

Abstract.

 In an infinite dimensional space, e.g. the set of infinite utility streams, there is no natural topology and the content of continuity is manipulable. Different desirable properties induce different topologies. We consider three properties: effectiveness. l ₁-summability and equity. In view of effectivity, the product topology is the most favourable one. The strict topology is the largest topology for which all the continuous linear maps are l ₁-summable. However, both topologies are myopic and conflict with the principle of equity. In case equity is desirable, the sup topology comes forward.