ISSN: 1304-7191 | E-ISSN: 1304-7205
On the rough hausdorff convergence
1Süleyman Demirel University, Department of Mathematics, Isparta, Turkey
Sigma J Eng Nat Sci 2021; 39(): 18-22 DOI: 10.14744/sigma.2021.00037
Full Text PDF

Abstract

Apreutesei [1] developed the concept of norm given with the help of the Hausdorff distance from a set to in the almost linear space. This space consists of sets that do not hold the inverse element property with respect to the Minkowski sum. In this paper, we first prove that the rough Hausdorff convergence of a sequence of sets to the set requires the rough convergence of the sequence of norms. Then we give the necessary and sufficient conditions for the rough convergence of the sequence to 0.