Abstract
A separation theorem, valid in infinite dimensional spaces, and involving the relative interior of the sets to be separated, will be extended to Fréchet spaces. This theorem will be elucidated by means of a few examples. The second separation theorem is a generalization of an existing separation theorem, valid in Fréchet spaces. This paper consists of two parts: part I contains the first theorem, the second part contains the second generalization.
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References
A. P. Robertson andW. J. Robertson,Topological vector spaces, Cambridge University Press, London (1973).
R. T. Rockefellar,Convex Analysis, Princeton University Press, New Jersey (1970).
J. Ponstein, Fenchel Duality in Banach spaces,Internal report OR-7607, Econometric Institute, University of Groningen (1976).
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Communicated by A. V. Balakrishnan
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Nieuwenhuis, J.W. Separating sets with relative interior in Fréchet spaces. Appl Math Optim 3, 373–376 (1976). https://doi.org/10.1007/BF01448187
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DOI: https://doi.org/10.1007/BF01448187