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Compactifications and uniformities on sigma frames

Joanne L. Walters-Wayland (1991)

Commentationes Mathematicae Universitatis Carolinae

A bijective correspondence between strong inclusions and compactifications in the setting of σ -frames is presented. The category of uniform σ -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 σ -frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined.

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