Approximate maps, filter monad, and a representation of localic maps

Bernhard Banaschewski; Aleš Pultr

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 4, page 285-298
  • ISSN: 0044-8753

Abstract

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A covariant representation of the category of locales by approximate maps (mimicking a natural representation of continuous maps between spaces in which one approximates points by small open sets) is constructed. It is shown that it can be given a Kleisli shape, as a part of a more general Kleisli representation of meet preserving maps. Also, we present the spectrum adjunction in this approximation setting.

How to cite

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Banaschewski, Bernhard, and Pultr, Aleš. "Approximate maps, filter monad, and a representation of localic maps." Archivum Mathematicum 046.4 (2010): 285-298. <http://eudml.org/doc/116492>.

@article{Banaschewski2010,
abstract = {A covariant representation of the category of locales by approximate maps (mimicking a natural representation of continuous maps between spaces in which one approximates points by small open sets) is constructed. It is shown that it can be given a Kleisli shape, as a part of a more general Kleisli representation of meet preserving maps. Also, we present the spectrum adjunction in this approximation setting.},
author = {Banaschewski, Bernhard, Pultr, Aleš},
journal = {Archivum Mathematicum},
keywords = {frames (locales); localic maps; approximation; Kleisli representation; frames; locales; localic maps; approximation; Kleisli representation},
language = {eng},
number = {4},
pages = {285-298},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Approximate maps, filter monad, and a representation of localic maps},
url = {http://eudml.org/doc/116492},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Banaschewski, Bernhard
AU - Pultr, Aleš
TI - Approximate maps, filter monad, and a representation of localic maps
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 4
SP - 285
EP - 298
AB - A covariant representation of the category of locales by approximate maps (mimicking a natural representation of continuous maps between spaces in which one approximates points by small open sets) is constructed. It is shown that it can be given a Kleisli shape, as a part of a more general Kleisli representation of meet preserving maps. Also, we present the spectrum adjunction in this approximation setting.
LA - eng
KW - frames (locales); localic maps; approximation; Kleisli representation; frames; locales; localic maps; approximation; Kleisli representation
UR - http://eudml.org/doc/116492
ER -

References

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  1. Banaschewski, B., Pultr, A., 10.1080/16073606.1996.9631828, Quaestiones Math. 19 (1–2) (1996), 101–127. (1996) Zbl0861.54023MR1390475DOI10.1080/16073606.1996.9631828
  2. Banaschewski, B., Pultr, A., 10.1007/s10485-006-9013-z, Appl. Categ. Structures 14 (2006), 165–190. (2006) Zbl1113.54013MR2247451DOI10.1007/s10485-006-9013-z
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  9. Kelley, J. L., General Topology, D. Van Nostrand Company, Inc., Toronto–New York–London, 1955. (1955) Zbl0066.16604MR0070144
  10. Lane, S. Mac, Categories for the Working Mathematician, Springer–Verlag, New York, 1971. (1971) MR1712872
  11. Manes, E., Algebraic Theories, Grad. Texts in Math. 26 (1976), 356 pp. (1976) Zbl0353.18007MR0419557
  12. Picado, J., Pultr, A., Sublocale sets and sublocale lattices, Arch. Math. (Brno) 42 (4) (2006), 409–418. (2006) Zbl1164.06313MR2283021
  13. Picado, J., Pultr, A., Locales treated mostly in a covariant way, vol. 41, Textos Mat. Ser. B, 2008. (2008) Zbl1154.06007MR2459570
  14. Priestley, H. A., Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 324 (1972), 507–530. (1972) Zbl0323.06011MR0300949
  15. Pultr, A., Handbook of Algebra, vol. 3, ch. Frames, pp. 791–858, Elsevier, 2003. (2003) MR2035108

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