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In [1], the authors have studied stability of certain causal properties ofspace-times in general relativity. As a continuation of this work, in thepresent paper, we review and discuss, some more aspects of stability whichoccur in various situations in the dynamics of general relativity. We arguethat not only choice of appropriate topology, but also the nature ofperturbation, like metric, matter or initial data, are key factors in decidingwhether a property is stable or not. We also study certain properties ofspace-times which are generic in an appropriate mathematical sense. Inparticular we argue that Linearization stability of a space-time is a genericproperty.

Role of Topologies in the Study of Dynamical Aspects of Stable and Generic Properties of Space-times in General Relativity