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Title of article :
Variational principles and topological games
Author/Authors :
Choban، نويسنده , , Mitrofan M. and Kenderov، نويسنده , , Petar S. and Revalski، نويسنده , , Julian P.، نويسنده ,
Issue Information :
دوماهنامه با شماره پیاپی سال 2012
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Abstract :
Let f be a bounded from below lower semicontinuous function defined in a completely regular topological space X. We show that there exists a continuous and bounded function g, defined in the same space, such that the perturbed function f + g attains its infimum in X. Moreover, the set of such good perturbations g (for which f + g attains its infimum) is dense in the space C ⁎ ( X ) of all bounded continuous functions in X with respect to the sup-norm. We give a sufficient condition under which this set of good perturbations contains a dense G δ -subset of C ⁎ ( X ) . The condition is in terms of existence of a winning strategy for one of the players in a certain topological game played in the space X. If the other player in the same game does not have a winning strategy, then the set of good perturbations is of the second Baire category in every open subset of C ⁎ ( X ) . The game we consider is similar to a game introduced by E. Michael in the study of completeness properties of topological spaces and to a game used by Kenderov and Moors to characterize fragmentability of topological spaces.
Keywords :
Topological game , Fragmentable space , variational principle , Tykhonov well-posedness
Journal title :
Topology and its Applications
Journal title :
Topology and its Applications
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