It is shown that the familiar description of the completion of a uniform frame in terms of its Samuel compactification can be extended to arbitrary nearness frames. This is achieved by means of the following new notion, a variant of compactness, for regular frames: such a frame will be called near-compact if it is complete in some totally bounded nearness. This leads to a natural concept of the Samuel near-compactification for arbitrary nearness frames which is then shown to play exactly the same role in the general setting which the Samuel compactification plays for uniform frames.
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Bernhard Banaschewski, Aleš Pultr, Completion and Samuel compactification of nearness and uniform frames. Port. Math. 69 (2012), no. 2, pp. 113–126DOI 10.4171/PM/1908