On completion in the category SSN$σ$Frm

Rok, strany: 2013, 201 - 214

We introduce the category $\mathbf{SSN}σ\mathbf{Frm}$ of super strong nearness \mbox{$σ$-frames} and show the existence of a completion for a super strong nearness \mbox{$σ$-frame} unique up to isomorphism by the similar construction presented in [WALTERS-WAYLAND, J. L.: \textit{Completeness and Nearly Fine Uniform Frames}. PhD Thesis, Univ. Catholique de Louvain, 1996] and [WALTERS-WAY-\linebreak LAND, J. L.: \textit{A Shirota Theorem for frames}, Appl. Categ. Structures \textbf{7} (1999), 271–277]. Completion is also shown to be a coreflection in $\mathbf{SSN}σ\mathbf{Frm}$. We also engage with the notion of total boundedness for nearness $σ$-frames and provide a characterization of the Samuel compactification of a nearness $σ$-frame alternative to the description in [NAIDOO, I.: \textit{Samuel compactification and uniform coreflection of nearness $σ $-frames}, Czechoslovak Math. J. \textbf{56(131)} (2006), 1229–1241].

ISO 690:

Naidoo, I. 2013. On completion in the category SSN$σ$Frm. In Mathematica Slovaca, vol. 63, no.2, pp. 201-214. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0093-y

APA:

Naidoo, I. (2013). On completion in the category SSN$σ$Frm. Mathematica Slovaca, 63(2), 201-214. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0093-y