Abstract

Ongoing research focuses on utilizing the existing generalized classes in nano semi-local functions within the framework of ideals. As part of this effort, we have successfully constructed and introduced new concepts and notions related to specific sets that address and handle semi-ideals within the space $\mathbb{N}_\star^X$. These new sets aim to expand the understanding and application of semi-ideal structures in this context.

      Additionally, further investigations are being carried out to explore semi-ideal nano topological spaces by leveraging the generalized classes already established in $\mathbb{N}_\star^X$. This research seeks to delve deeper into the properties, behavior, and potential applications of these spaces. Through this, we aim to develop a more comprehensive framework that integrates semi-ideal concepts into nano topology, thereby enriching the theoretical and practical dimensions of the field.

Keywords and Phrases

$_\mathbb{S}\mathbb{I}^n_t$-set, $_\mathbb{S}\mathbb{I}^n_{t_\alpha}$-set, $_\mathbb{S}\mathbb{I}^n_\mathcal{R}$-set, $_\mathbb{S}\mathbb{I}^n_{\mathcal{R}_\alpha}$-set, $_\mathbb{S}\mathbb{I}^n_{t^\#}$-set, $_\mathbb{S}\mathbb{I}^n_{t_\alpha^\#}$-set, $_\mathbb{S}\mathbb{I}^n_{\mathcal{R}^\#}$-set, $_\mathbb{S}\mathbb{I}^n_{\mathcal{R}_\alpha^\#}$-set and $_\mathbb{S}\mathbb{I}^n_{\mathcal{S}\mathcal{R}}$-set.

A.M.S. subject classification

54A10, 54C05, 54C08, 54C10.

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