Abstract

We obtain new closedness conditions for linear images and vector sums of sets in finite-dimensional vector spaces and illustrate their relations with the existing results on the subject. These new conditions use the concept of asymptotic plane and are applicable to the case of arbitrary (not only convex) sets.

Author information

Contact details are reproduced from the original publication and may be historical.

Valeriu Soltan

Dept. of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, U.S.A.

vsoltan@gmu.edu

Keywords

  • Asymptotic cone
  • asymptotic plane
  • closedness condition
  • lineality space
  • linear image
  • recession cone
  • vector sum

Mathematics Subject Classification

52A20, 49M45, 90C25

Suggested citation

V. Soltan. “Asymptotic Planes and Closedness Conditions for Linear Images and Vector Sums of Sets.” Journal of Convex Analysis 25 (2018), No. 4, 1183–1196. https://doi.org/10.68381/jca25074

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.