Biframe compactifications

Anneliese Schauerte

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 3, page 567-574
  • ISSN: 0010-2628

Abstract

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Compactifications of biframes are defined, and characterized internally by means of strong inclusions. The existing description of the compact, zero-dimensional coreflection of a biframe is used to characterize all zero-dimensional compactifications, and a criterion identifying them by their strong inclusions is given. In contrast to the above, two sufficient conditions and several examples show that the existence of smallest biframe compactifications differs significantly from the corresponding frame question.

How to cite

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Schauerte, Anneliese. "Biframe compactifications." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 567-574. <http://eudml.org/doc/247485>.

@article{Schauerte1993,
abstract = {Compactifications of biframes are defined, and characterized internally by means of strong inclusions. The existing description of the compact, zero-dimensional coreflection of a biframe is used to characterize all zero-dimensional compactifications, and a criterion identifying them by their strong inclusions is given. In contrast to the above, two sufficient conditions and several examples show that the existence of smallest biframe compactifications differs significantly from the corresponding frame question.},
author = {Schauerte, Anneliese},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {biframe compactification; strong inclusion; strong inclusions; biframe compactifications},
language = {eng},
number = {3},
pages = {567-574},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Biframe compactifications},
url = {http://eudml.org/doc/247485},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Schauerte, Anneliese
TI - Biframe compactifications
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 3
SP - 567
EP - 574
AB - Compactifications of biframes are defined, and characterized internally by means of strong inclusions. The existing description of the compact, zero-dimensional coreflection of a biframe is used to characterize all zero-dimensional compactifications, and a criterion identifying them by their strong inclusions is given. In contrast to the above, two sufficient conditions and several examples show that the existence of smallest biframe compactifications differs significantly from the corresponding frame question.
LA - eng
KW - biframe compactification; strong inclusion; strong inclusions; biframe compactifications
UR - http://eudml.org/doc/247485
ER -

References

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  1. Banaschewski B., Compact regular frames and the Sikorski theorem, Kyungpook Math. J. 28 (1988), 1-14. (1988) Zbl0676.03029MR0986848
  2. Banaschewski B., Universal zero-dimensional compactifications, Categorical Topology and its Relations to Modern Analysis, Algebra and Combinatorics (Prague, 1988), 257-269, World Sci. Publishing, Teaneck, NJ, 1989. MR1047906
  3. Banaschewski B., Compactification of frames, Math. Nachr. 149 (1990), 105-116. (1990) Zbl0722.54018MR1124796
  4. Banaschewski B., Biframe compactifications, manuscript, 1989. 
  5. Banaschewski B., Brümmer G.C.L., Stably continuous frames, Math. Proc. Cambr. Phil. Soc. 104 (1988), 7-19. (1988) MR0938448
  6. Banaschewski B., Brümmer G.C.L., Hardie K.A., Biframes and bispaces, Quaestiones Math. 6 (1983), 13-25. (1983) MR0700237
  7. Bourbaki N., General Topology, Addison Wesley Publishing Company, Reading, Massachussetts, 1966. Zbl1107.54001
  8. Johnstone P.T., Stone Spaces, Cambridge Univ. Press, Cambridge, 1982. Zbl0586.54001MR0698074
  9. Schauerte A., Biframes, Ph.D. Thesis, McMaster University, 1992. 

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