Record number :

1583556

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

Pages :

13

From page :

3550

To page :

3562

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

Serial Year :

2012

Link To Document :