Realcompactification of frames

Nizar Marcus

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 2, page 347-356
  • ISSN: 0010-2628

Abstract

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We give a construction of Wallman-type realcompactifications of a frame L by considering regular sub σ -frames the join of which generates L . In particular, we show that the largest such regular sub σ -frame gives rise to the universal realcompactification of L .

How to cite

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Marcus, Nizar. "Realcompactification of frames." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 347-356. <http://eudml.org/doc/247722>.

@article{Marcus1995,
abstract = {We give a construction of Wallman-type realcompactifications of a frame $L$ by considering regular sub $\sigma $-frames the join of which generates $L$. In particular, we show that the largest such regular sub $\sigma $-frame gives rise to the universal realcompactification of $L$.},
author = {Marcus, Nizar},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {frame; $\sigma $-frame; realcompactification; regular sigma-frame; realcompactification; realcompactness},
language = {eng},
number = {2},
pages = {347-356},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Realcompactification of frames},
url = {http://eudml.org/doc/247722},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Marcus, Nizar
TI - Realcompactification of frames
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 347
EP - 356
AB - We give a construction of Wallman-type realcompactifications of a frame $L$ by considering regular sub $\sigma $-frames the join of which generates $L$. In particular, we show that the largest such regular sub $\sigma $-frame gives rise to the universal realcompactification of $L$.
LA - eng
KW - frame; $\sigma $-frame; realcompactification; regular sigma-frame; realcompactification; realcompactness
UR - http://eudml.org/doc/247722
ER -

References

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  1. Banaschewski B., Gilmour C.R.A., Stone-Čech compactification and dimension theory for regular σ -frames, J. London Math. Soc. 39 (1989), 1-8. (1989) Zbl0675.06005MR0989914
  2. Gilmour C.R.A., Realcompactifications through zero-set spaces, Quaestiones Math. 6 (1983), 73-95. (1983) Zbl0521.54012MR0700241
  3. Gilmour C.R.A., Realcompact spaces and regular σ -frames, Math. Proc. Camb. Phil. Soc. 96 (1984), 73-79. (1984) Zbl0547.54021MR0743702
  4. Johnstone P.T., Stone Spaces, Cambridge Studies in Advanced Math. 3, Cambridge Univ. Press, 1982. Zbl0586.54001MR0698074
  5. Madden J., Vermeer J., Lindelöf locales and realcompactness, Math. Proc. Camb. Phil. Soc. 99 (1986), 473-480. (1986) Zbl0603.54021MR0830360
  6. G. Schlitt, ℕ -Compact frames and applications, Doctoral thesis, McMaster University, 1990. MR1118300

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