Completion and Samuel compactification of nearness and uniform frames
Bernhard BanaschewskiMcMaster University, Hamilton, Canada
Aleš PultrCharles University, Prague, Czech Republic
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.
Cite this article
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