Abstract
Let X be a complete metric space. According to Baire’s theorem, the intersection of every countable collection of open dense subsets of X is dense in X. This rather simple, yet powerful result has found many applications. In particular, given a property which elements of X may have, it is of interest to determine whether this property is generic, that is, whether the set of elements which do enjoy this property contains a countable intersection of open dense sets. Such an approach, when a certain property is investigated for the whole space X and not just for a single point in X, has already been successfully applied in many areas of Analysis. We mention, for instance, the theory of dynamical systems [12, 18, 24, 35, 33, 52], optimization [22, 44], variational analysis [2, 9], [20, 211, the calculus of variations [4, 14, 55] and optimal control [56, 57].
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Reich, S., Zaslavski, A.J. (2001). Generic Aspects of Metric Fixed Point Theory. In: Kirk, W.A., Sims, B. (eds) Handbook of Metric Fixed Point Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1748-9_16
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DOI: https://doi.org/10.1007/978-94-017-1748-9_16
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