N-compact frames

Schlitt, Greg M.. "N-compact frames." Commentationes Mathematicae Universitatis Carolinae 32.1 (1991): 173-187. <http://eudml.org/doc/247258>.

@article{Schlitt1991,
abstract = {We investigate notions of $\mathbb \{N\}$-compactness for frames. We find that the analogues of equivalent conditions defining $\mathbb \{N\}$-compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘$\mathbb \{N\}$-cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial $\mathbb \{N\}$-compactness form a much larger class, and better embody what ‘$\mathbb \{N\}$-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 ‘$\mathbb \{N\}$-compactifications’), which both restrict to the spatial $\mathbb \{N\}$-compactification.},
author = {Schlitt, Greg M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {frame; locale; complete Heyting algebra; $\mathbb \{N\}$-compact; Lindelöf locales; -compactness; Stone -compact locales; Herrlich -compact locales},
language = {eng},
number = {1},
pages = {173-187},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {N-compact frames},
url = {http://eudml.org/doc/247258},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Schlitt, Greg M.
TI - N-compact frames
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 1
SP - 173
EP - 187
AB - We investigate notions of $\mathbb {N}$-compactness for frames. We find that the analogues of equivalent conditions defining $\mathbb {N}$-compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘$\mathbb {N}$-cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial $\mathbb {N}$-compactness form a much larger class, and better embody what ‘$\mathbb {N}$-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 ‘$\mathbb {N}$-compactifications’), which both restrict to the spatial $\mathbb {N}$-compactification.
LA - eng
KW - frame; locale; complete Heyting algebra; $\mathbb {N}$-compact; Lindelöf locales; -compactness; Stone -compact locales; Herrlich -compact locales
UR - http://eudml.org/doc/247258
ER -