Structure of the rough Hausdorff limit set of sequences of balls in normed spaces

Öznur Ölmez, Erdinç Dündar

Abstract


In this paper, we study the rough Hausdorff convergence of a sequence (B_{n}) of balls in normed spaces. We also discuss the following questions:
(Q₁) Does the rough Hausdorff limit set of the sequence (B_{n}) consist of balls?
(Q₂) Is the set of intersections or unions of sets taken from the rough Hausdorff limit set of the sequence (B_{n}) a ball?


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