Booleanization of uniform frames

Bernhard Banaschewski; Aleš Pultr

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 1, page 135-146
  • ISSN: 0010-2628

Abstract

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Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.

How to cite

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Banaschewski, Bernhard, and Pultr, Aleš. "Booleanization of uniform frames." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 135-146. <http://eudml.org/doc/247936>.

@article{Banaschewski1996,
abstract = {Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.},
author = {Banaschewski, Bernhard, Pultr, Aleš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Booleanization; uniform frame; uniform space; weakly open maps and homomorphisms; functoriality; Booleanization of frames; weakly open morphisms; uniform frames; reflection},
language = {eng},
number = {1},
pages = {135-146},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Booleanization of uniform frames},
url = {http://eudml.org/doc/247936},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Banaschewski, Bernhard
AU - Pultr, Aleš
TI - Booleanization of uniform frames
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 135
EP - 146
AB - Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.
LA - eng
KW - Booleanization; uniform frame; uniform space; weakly open maps and homomorphisms; functoriality; Booleanization of frames; weakly open morphisms; uniform frames; reflection
UR - http://eudml.org/doc/247936
ER -

References

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  9. Johnstone P.T., Stone Spaces, Cambridge University Press, Cambridge, 1982. Zbl0586.54001MR0698074
  10. Johnstone P.T., Factorization theorems for geometric morphisms, II., Springer Lecture Notes in Math. 915 (1982), 216-233. (1982) Zbl0477.18006MR0659894
  11. Kříž I., A direct description of uniform completion in locales and a characterization of LT groups, Cahiers Top. et Géom. Diff. Cat. 27 (1986), 19-34. (1986) MR0845407
  12. Mioduszewski J., Rudolf L., H-closed and extremally disconnected Hausdorff spaces, Dissertationes Math. 66 (1969). (1969) Zbl0204.22404MR0256353
  13. Vickers S., Topology via Logic, Cambridge Tracts in Theor. Comp. Sci., Number 5, Cambridge University Press, Cambridge, 1985. Zbl0922.54002MR1002193

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