Topology control is a well-known strategy to save energy and extend the lifetime of wireless sensor networks. In the literature, it is usually referred as the process that, given a set of nodes, builds a reduced topology that still guarantees connectivity and coverage. Here, we extend this definition. We consider topology control as two processes: topology construction and topology maintenance. Topology construction encompasses those algorithms that build the reduced topology. Topology maintenance is the process that changes the reduced topology from time to time when the current one is no longer optimal. In this paper we define topology maintenance and present different strategies and triggering criteria that can be used to switch the network topology. We also implement static and dynamic global topology maintenance strategies using two well-known topology construction algorithms and time- and energy-based triggering criteria, and compare their performance via simulations on sparse and dense networks. Our results demonstrate that the appropriate use of topology maintenance techniques extends the network lifetime versus the option of not doing topology maintenance at all. In sparse networks, while dynamic global techniques improve the network lifetime, static techniques may improve or degrade the performance. However, all results are fairly similar. On the other hand, topology maintenance is very well justified in dense networks where important performance improvements can be achieved. In this case, the superiority of dynamic global techniques is evident, and even more as the density of the network increases.