Geodesic
Compactifications and uniformities on sigma frames
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 1, pp. 189-198.

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A bijective correspondence between strong inclusions and compactifications in the setting of $\sigma$-frames is presented. The category of uniform $\sigma$-frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the $\sigma$-frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined.
Classification : 18B35, 54D35, 54E05, 54E52, 54J05
Keywords: strong inclusion; compactification; uniform $\sigma$-frame; uniform cozero 
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Walters, Joanne. Compactifications and uniformities on sigma frames. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 1, pp. 189-198. http://geodesic.mathdoc.fr/item/CMUC_1991__32_1_a18/