Metrizable completely distributive lattices

Zhang De-Xue

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 1, page 137-148
  • ISSN: 0010-2628

Abstract

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The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.

How to cite

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De-Xue, Zhang. "Metrizable completely distributive lattices." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 137-148. <http://eudml.org/doc/248103>.

@article{De1997,
abstract = {The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.},
author = {De-Xue, Zhang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {completely distributive lattice; interval topology; AR; ANR; completely distributive lattice; continuous lattice; interval topology; retract; absolute (neighborhood) retract},
language = {eng},
number = {1},
pages = {137-148},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Metrizable completely distributive lattices},
url = {http://eudml.org/doc/248103},
volume = {38},
year = {1997},
}

TY - JOUR
AU - De-Xue, Zhang
TI - Metrizable completely distributive lattices
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 1
SP - 137
EP - 148
AB - The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.
LA - eng
KW - completely distributive lattice; interval topology; AR; ANR; completely distributive lattice; continuous lattice; interval topology; retract; absolute (neighborhood) retract
UR - http://eudml.org/doc/248103
ER -

References

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  2. Gierz G. et al., A Compendium of Continuous Lattices, Springer-Verlag, 1980. Zbl0452.06001MR0614752
  3. van Gool F., Lower semicontinuous functions with values in a continuous lattice, Comment. Math. Univ. Carolinae 33 (1992), 505-523. (1992) Zbl0769.06005MR1209292
  4. Hu S.T., Theory of Retracts, Wayne State University Press, 1965. Zbl1164.54341MR0181977
  5. Johnstone P.T., Stone Spaces, Cambridge University Press, 1982. Zbl0586.54001MR0698074
  6. Katětov M., On real-valued functions in topological spaces, Fund. Math. 38 (1951), 85-91 Correction in Fund. Math. 40 (1953), 203-205. (1953) MR0050264
  7. Liu Ying-Ming et al., Topological and analytic characterizations of completely distributive law, Sci. Bull. 35 (1990), 1223-1226. (1990) 
  8. Liu Ying-Ming, Luo Mao-Kang, Lattice-valued Hahn-Diedonne-Tong insertion theorem and stratification structure, Topology Appl. 45 (1992), 173-188. (1992) MR1180808
  9. Steen L.A., Seebach J.A., Jr., Counterexamples in topology, second edition, Springer-Verlag, 1978. Zbl0386.54001MR0507446
  10. Tong H., Some characterizations of normal and perfectly normal spaces, Duke Math. J. 19 (1952), 289-292. (1952) Zbl0046.16203MR0050265
  11. Xu Luo-Shan, Research on lattice and topology, PhD. Dissertation of Sichuan University, 1992. 
  12. Zhang De-Xue, Continuous lattices and spaces of semicontinuous functions, preprint. 

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