A Study on $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ Uniform $\mathtt{Ir}^{*}$ Centred Structure Compactification

Abstract

Compactification is one of the novel extensions in topological spaces. Nets and filters are used to study the detailed characterization of compactness and convergence in topological spaces. The major framework of this article delves into $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ uniform $\mathtt{Ir}^{*}$ centred structure compactification.This introduces an innovative space that integrates a $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ uniform topological space with a $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ uniform $\mathtt{Ir}^{*}$ space. It explores the irreducibility in $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ uniform topological spaces and combines with a $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ uniform centred system that addresses the intersection of open sets.This study also involves $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ uniform $\mathtt{Ir}^{}$ centred structure filters and $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ uniform $\mathtt{Ir}^{}$ centred structure nets, which provide a detailed analysis of sequences and their convergence in $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ uniform topological spaces.