Sublocale sets and sublocale lattices

Jorge Picado; Aleš Pultr

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 4, page 409-418
  • ISSN: 0044-8753

Abstract

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We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.

How to cite

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Picado, Jorge, and Pultr, Aleš. "Sublocale sets and sublocale lattices." Archivum Mathematicum 042.4 (2006): 409-418. <http://eudml.org/doc/249828>.

@article{Picado2006,
abstract = {We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.},
author = {Picado, Jorge, Pultr, Aleš},
journal = {Archivum Mathematicum},
keywords = {frames; sublocales; coframe of sublocales; fitness and subfitness; frames; sublocales; coframe of sublocales; fitness and subfitness},
language = {eng},
number = {4},
pages = {409-418},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Sublocale sets and sublocale lattices},
url = {http://eudml.org/doc/249828},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Picado, Jorge
AU - Pultr, Aleš
TI - Sublocale sets and sublocale lattices
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 4
SP - 409
EP - 418
AB - We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.
LA - eng
KW - frames; sublocales; coframe of sublocales; fitness and subfitness; frames; sublocales; coframe of sublocales; fitness and subfitness
UR - http://eudml.org/doc/249828
ER -

References

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  1. Davey B. A., Priestley H. A., Introduction to Lattices and Order, Second Edition, Cambridge University Press, 2001. Zbl1002.06001MR1902334
  2. Isbell J. R., Atomless parts of spaces, Math. Scand. 31 (1972), 5–32. (1972) Zbl0246.54028MR0358725
  3. Johnstone P. T., Stone Spaces, Cambridge Stud. Adv. Math. No 3, Cambridge University Press, 1983. (1983) MR0698074
  4. Mac Lane S., Categories for the Working Mathematician, Springer-Verlag, New York, 1971. (1971) Zbl0232.18001MR0354798
  5. Picado J., Pultr A., Tozzi A., Locales, In: M. C. Pedicchio and W. Tholen (Eds.), Categorical Foundations - Special Topics in Order, Topology, Algebra and Sheaf Theory, Encyclopedia of Mathematics and its Applications, Vol. 97, Cambridge University Press, 2003, pp. 49–101. Zbl1080.06010MR2056581
  6. Priestley H. A., Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2 (1970), 186–190. (1970) Zbl0201.01802MR0265242
  7. Priestley H. A., Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 324 (1972), 507–530. (1972) Zbl0323.06011MR0300949
  8. Pultr A., Sichler J., Frames in Priestley duality, Cahiers Topologie Géom. Différentielle Catég. XXIX (1988), 193–202. (1988) MR0975372
  9. Pultr A., Sichler J., A Priestley view of spatialization of frames, Cahiers Topologie Géom. Différentielle Catég. XLI (2000), 225–238. Zbl0970.06006MR1784219
  10. Simmons H., The lattice theoretic part of topological separation properties, Proc. Edinburgh Math. Soc. (2) 21 (1978), 41–48. (1978) Zbl0396.54014MR0493959

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