Slowly oscillating sequences in locally normal Riesz spaces

Abstract

In the present paper, we are going to introduce and at the same time investigate the notion of slowly oscillating sequences, study on slowly oscillating compactness and slowly oscillating continuous functions in locally normal Riesz space. For this purpose, first of all, we are going to try to put forward some fundamental theorems about oscillating continuity, slowly oscillating compactness, sequential continuity and uniform continuity. Secondly, the newly obtained results in this paper can also be obtained with the definition of quasi-slowly oscillating and.-quasi-slowly oscillating sequences in terms of fuzzy points. Finally, most of the related theorems and lemmas are presented clearly.