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An extension of a theorem of Jeroslow and Kortanek

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Abstract

Given a semi-infinite system of linear inequalities, including strict inequalities, it is shown that if every finite subsystem has a solution inR, then the entire system has a solution in the ordered fieldR(M) obtained by adjoining a transcendental greater than every real number.

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References

  1. R. G. Jeroslow, and K. O. KortanekOn semi-infinite systems of linear inequalities, Israel J. Math.10 (1971), 252–259.

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  2. J. Stoer and C. Witzgall,Convexity and Optimization in Finite Dimensions I, Springer-Verlag, New York, 1970.

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  3. R. J. Duffin,Infinite programs, Linear Inequalities and Related Systems, Kuhn and Tucker (eds.), Princeton University Press, 1956.

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Authors and Affiliations

  1. Department of Mathematics, Carnegie-Mellon University, Pittsburg, Pennsylvania, USA

    C. E. Blair

Authors
  1. C. E. Blair
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Additional information

This work was supported in part by NSF Grant GJ-28457X1.

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Blair, C.E. An extension of a theorem of Jeroslow and Kortanek. Israel J. Math. 17, 111–115 (1974). https://doi.org/10.1007/BF02756833

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  • DOI: https://doi.org/10.1007/BF02756833

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