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A topological characterization for closed sets under polar duality in ℚn

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Abstract

A topological characterization is given for closed sets in ℚn under the restriction of (cone) polar duality to ℚn.

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References

  1. P.C.P. Carvalho and L.E. Trotter, Jr., “An abstract linear duality model,”Mathematics of Operations Research 14 (1989) 639–663.

    Google Scholar 

  2. J.D. Dixon, “On duality theorems,”Linear Algebra and its Applications 39 (1981) 223–228.

    Google Scholar 

  3. R.G. Jeroslow, “Some structure and basis theorems for integral monoids,” Management Sciences Research Report No. 367, Graduate School of Industrial Administration, Carnegie-Mellon University (Pittsburgh, PA, 1975).

    Google Scholar 

  4. R.G. Jeroslow, “Some basis theorems for integral monoids,”Mathematics of Operations Research 3 (1978) 145–154.

    Google Scholar 

  5. R.T. Rockafeller,Convex Analysis (Princeton University Press, Princeton, NJ, 1970).

    Google Scholar 

  6. J. Stoer and C. Witzgall,Convexity and Optimization in Finite Dimensions I (Springer, Berlin, 1970).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, The Johns Hopkins University, 21218, Baltimore, MD, USA

    M. Hartmann

  2. School of Operations Research and Industrial Engineering, Cornell University, 14853, Ithaca, NY, USA

    L. E. Trotter Jr.

  3. Division of Building Materials, National Institute of Standards and Technology, 20899, Gaithersburg, MD, USA

    M. Hartmann

Authors
  1. M. Hartmann
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  2. L. E. Trotter Jr.
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Hartmann, M., Trotter, L.E. A topological characterization for closed sets under polar duality in ℚn . Mathematical Programming 49, 281–283 (1990). https://doi.org/10.1007/BF01588793

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  • DOI: https://doi.org/10.1007/BF01588793

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