Geodesic
Samuel compactification and uniform coreflection of nearness $\sigma$-frames
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 4, pp. 1229-1241 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We introduce the structure of a nearness on a $\sigma $-frame and construct the coreflection of the category ${\mathbf N\sigma Frm}$ of nearness $\sigma $-frames to the category ${\mathbf KReg\sigma Frm}$ of compact regular $\sigma $-frames. This description of the Samuel compactification of a nearness $\sigma $-frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform $\sigma $-frames in [11]. We also construct the uniform coreflection of a nearness $\sigma $-frame, that is, the coreflection of the category of ${\mathbf N\sigma Frm}$ to the category U$\sigma $Frm of uniform $\sigma $-frames.
We introduce the structure of a nearness on a $\sigma $-frame and construct the coreflection of the category ${\mathbf N\sigma Frm}$ of nearness $\sigma $-frames to the category ${\mathbf KReg\sigma Frm}$ of compact regular $\sigma $-frames. This description of the Samuel compactification of a nearness $\sigma $-frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform $\sigma $-frames in [11]. We also construct the uniform coreflection of a nearness $\sigma $-frame, that is, the coreflection of the category of ${\mathbf N\sigma Frm}$ to the category U$\sigma $Frm of uniform $\sigma $-frames.
Classification : 06D22, 18B35, 54D35, 54E17
Keywords: $\sigma $-frame; nearness; Samuel compactification 
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Naidoo, Inderasan. Samuel compactification and uniform coreflection of nearness $\sigma$-frames. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 4, pp. 1229-1241. http://geodesic.mathdoc.fr/item/CMJ_2006_56_4_a11/

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