ON $\mathcal{I}^{\mathcal{K}}$-SUPREMUM, $\mathcal{I}^{\mathcal{K}}$-INFIMUM AND RELATED RESULTS

Abstract

In this paper, we introduce the concept of $\mathcal{I}^{\mathcal{K}}$-supremum, $\mathcal{I}^{\mathcal{K}}$-infimum, $\mathcal{I}^{\mathcal{K}}$-limit superior, and $\mathcal{I}^{\mathcal{K}}$-limit inferior and investigate a few implication relationships between them.

Keywords

• ideal
• filter
• $\mathcal{i}^{\mathcal{k}}$-supremum
• $\mathcal{i}^{\mathcal{k}}$-infimum
• $\mathcal{i}^{\mathcal{k}}$-limit superior
• $\mathcal{i}^{\mathcal{k}}$-limit inferior