A new look at pointfree metrization theorems

Bernhard Banaschewski; Aleš Pultr

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 167-175
  • ISSN: 0010-2628

Abstract

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We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.

How to cite

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Banaschewski, Bernhard, and Pultr, Aleš. "A new look at pointfree metrization theorems." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 167-175. <http://eudml.org/doc/248278>.

@article{Banaschewski1998,
abstract = {We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.},
author = {Banaschewski, Bernhard, Pultr, Aleš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {frame; (metric) diameter; metrization; frame; diameter; metrization},
language = {eng},
number = {1},
pages = {167-175},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A new look at pointfree metrization theorems},
url = {http://eudml.org/doc/248278},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Banaschewski, Bernhard
AU - Pultr, Aleš
TI - A new look at pointfree metrization theorems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 167
EP - 175
AB - We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.
LA - eng
KW - frame; (metric) diameter; metrization; frame; diameter; metrization
UR - http://eudml.org/doc/248278
ER -

References

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  1. Engelking R., General Topology, Sigma Series in Pure Mathematics, Vol.6, Helderman Verlag, Berlin, 1989. Zbl0684.54001MR1039321
  2. Isbell J.R., Atomless parts of spaces, Math. Scand. 31 (1972), 5-32. (1972) Zbl0246.54028MR0358725
  3. Isbell J.R., Graduation and dimension in locales, in: Aspects of Topology, London MS Lecture Notes 93 (1985), 195-210. (1985) Zbl0555.54020MR0787829
  4. Johnstone P.T., Stone Spaces, Cambridge University Press, Cambridge, 1982. Zbl0586.54001MR0698074
  5. Kaiser T., A sufficient condition of full normality, Comment Math. Univ. Carolinae 37 (1996), 381-389. (1996) Zbl0847.54025MR1399010
  6. Pultr A., Pointless uniformities II. (Dia)metrization, Comment. Math. Univ. Carolinae 25 (1984), 105-120. (1984) MR0749119
  7. Pultr A., Remarks on metrizable locales, Suppl. Rend. Circ. Mat. Palermo 6 (1984), 247-258. (1984) Zbl0565.54001MR0782722
  8. Pultr A., Diameters in locales: How bad they can be, Comment. Math. Univ. Carolinae 29 (1988), 731-742. (1988) Zbl0668.06008MR0982793
  9. Pultr A., Úlehla J., Notes on characterization of paracompact frames, Comment. Math. Univ. Carolinae 30 (1989), 377-384. (1989) MR1014137
  10. Sun Shu-Hao, On paracompact locales and metric locales, Comment. Math. Univ. Carolinae 30 (1989), 101-107. (1989) MR0995708
  11. Vickers S., Topology via Logic, Cambridge Tracts in Theor. Comp. Sci., Number 5, Cambridge University Press, Cambridge, 1985. Zbl0922.54002MR1002193

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