N-compact frames
Schlitt, Greg M.
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 173-187 / Harvested from Czech Digital Mathematics Library
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We investigate notions of $\Bbb N$-compactness for frames. We find that the analogues of equivalent conditions defining $\Bbb N$-compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame `$\Bbb N$-cubes' are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial $\Bbb N$-compactness form a much larger class, and better embody what `$\Bbb N$-compact frames' should be. This latter property is expressible without reference to maximal ideals or filters. We construct the co-reflections for both of the classes, (the `$\Bbb N$-compactifications'), which both restrict to the spatial $\Bbb N$-compactification.

Publié le : 1991-01-01
Classification:  06A23,  06D20,  06D99,  18B30,  54A05,  54D20 
@article{116953,
     author = {Greg M. Schlitt},
     title = {N-compact frames},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {173-187},
     zbl = {0747.06009},
     mrnumber = {1118300},
     language = {en},
     url = {http://dml.mathdoc.fr/item/116953}
}

Schlitt, Greg M. N-compact frames. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 173-187. http://gdmltest.u-ga.fr/item/116953/

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