Abstract: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.
Keywords: strong inclusion, compactification, uniform $\sigma $-frame, uniform cozero
AMS Subject Classification: 18B35, 54D35, 54E52, 54J05