Remarks on the sobriety of Scott topology and weak topology on posets

He Wei; Jiang Shouli

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 3, page 531-535
  • ISSN: 0010-2628

Abstract

top
We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].

How to cite

top

Wei, He, and Shouli, Jiang. "Remarks on the sobriety of Scott topology and weak topology on posets." Commentationes Mathematicae Universitatis Carolinae 43.3 (2002): 531-535. <http://eudml.org/doc/248972>.

@article{Wei2002,
abstract = {We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].},
author = {Wei, He, Shouli, Jiang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sober topological space; Scott topology; weak topology; sober topological space; Scott topology; weak topology},
language = {eng},
number = {3},
pages = {531-535},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Remarks on the sobriety of Scott topology and weak topology on posets},
url = {http://eudml.org/doc/248972},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Wei, He
AU - Shouli, Jiang
TI - Remarks on the sobriety of Scott topology and weak topology on posets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 3
SP - 531
EP - 535
AB - We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].
LA - eng
KW - sober topological space; Scott topology; weak topology; sober topological space; Scott topology; weak topology
UR - http://eudml.org/doc/248972
ER -

References

top
  1. Isbell J.R., Function spaces and adjoints, Math. Scand. 36 (1975), 317-339. (1975) Zbl0309.54016MR0405340
  2. Hoffmann R.-E., Essentially complete T 0 spaces, Manuscripta Math. 27 (1979), 401-432. (1979) Zbl0418.54020MR0534803
  3. Isbell J.R., Completion of a construction of Johnstone, Proc. Amer. Math. Soc. 85 (1982), 333-334. (1982) Zbl0492.06006MR0656096
  4. Gierz G., Hoffmann K.H., Keimel K., Lawson J.D., Mislove M., Scott D.S., A Compendium of Continuous Lattices, Springer-Verlag, 1980. MR0674650
  5. Johnstone P.T., Scott is not always sober, Lecture Notes in Math. 871, Springer-Verlag, 1981, pp.282-283. Zbl0469.06002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.