On the sustainability of an activity

This paper develops a framework to determine the sustainability of a general activity. We define an activity as an action or process that uses one or more resources and that responds either wholly or partially to a demand. A definition for sustainability is developed and is contingent on whether or not an activity can be sustained according to the available resources, the duration of an activity, the cost of its execution, or whether substitution is possible. A sustainability condition is met when the duration, cost and the chain of dependent activities satisfies the demand. Two conditions for sustainability are developed: a strong condition when the demand is met with no substitution and a weak condition when the demand is met via substitution. In the latter case, we show that the set of all sustainable activities is a subset of a N-level union of sustainable activities and forms a topological cover.