Extending asymmetric convergence and Cauchy condition using ideals (Q2843884)

The authors use the notion of ideals to extend the convergence and Cauchy conditions in asymmetric metric spaces. The asymmetry (or rather absence of symmetry) of these spaces makes the whole treatment different from the metric case and they use a genuinely asymmetric condition called (AMA) to prove many results and show that certain classic results fail in the asymmetric context if the assumption is dropped.NEWLINENEWLINEThe paper is organized as follows. In Section 2, basic definitions and notions are described. In Section 3, the forward and backward \(I\) and \(I^{\ast}\) asymmetric \(I\)-Cauchy condition is discussed. Finally in Section 5, the asymmetric \(I^{\ast}\)-Cauchy condition is introduced and open problems are stated.