Abstract
We study generic variational principles in optimization when the underlying topological space X is not necessarily metrizable. It turns out that, to ensure the validity of such a principle, instead of having a complete metric which generates the topology in the space X (which is the case of most variational principles), it is enough that we dispose of a complete metric on X which is stronger than the topology in X and fragments the space X.
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Acknowledgements
Both authors have been partially supported by the Bulgarian National Fund for Scientific Research, under grant DO02-360/2008.
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The results in this article have been obtained while the second named author was professeur associé in the group LAMIA of the Department of Mathematics and Informatics of the Université des Antilles et de la Guyane, Guadeloupe, France.
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Kenderov, P.S., Revalski, J.P. Variational principles in non-metrizable spaces. TOP 20, 467–474 (2012). https://doi.org/10.1007/s11750-011-0243-3
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DOI: https://doi.org/10.1007/s11750-011-0243-3