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Journal of Convex Analysis 25 (2018), No. 4, 1183--1196
Copyright Heldermann Verlag 2018

Asymptotic Planes and Closedness Conditions for Linear Images and Vector Sums of Sets

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

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.

Keywords: Asymptotic cone, asymptotic plane, closedness condition, lineality space, linear image, recession cone, vector sum.

MSC: 52A20, 49M45, 90C25

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