A note on topology of Z -continuous posets

Venu G. Menon

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 4, page 821-824
  • ISSN: 0010-2628

Abstract

top
Z -continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of Z -continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a Z -continuous poset is defined and its properties are explored.

How to cite

top

Menon, Venu G.. "A note on topology of $Z$-continuous posets." Commentationes Mathematicae Universitatis Carolinae 37.4 (1996): 821-824. <http://eudml.org/doc/247900>.

@article{Menon1996,
abstract = {$Z$-continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of $Z$-continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a $Z$-continuous poset is defined and its properties are explored.},
author = {Menon, Venu G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$Z$-continuous posets; intrinsic topology; -continuous posets; intrinsic topology},
language = {eng},
number = {4},
pages = {821-824},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on topology of $Z$-continuous posets},
url = {http://eudml.org/doc/247900},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Menon, Venu G.
TI - A note on topology of $Z$-continuous posets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 4
SP - 821
EP - 824
AB - $Z$-continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of $Z$-continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a $Z$-continuous poset is defined and its properties are explored.
LA - eng
KW - $Z$-continuous posets; intrinsic topology; -continuous posets; intrinsic topology
UR - http://eudml.org/doc/247900
ER -

References

top
  1. Bandelt H.J., Erné M., The category of Z -continuous posets, J. Pure Appl. Algebra 30 (1983), 219-226. (1983) MR0724033
  2. Gierz G., Hofmann K.H., Keimel K., Lawson J.D., Mislove M., Scott D.S., A Compendium of Continuous Lattices, Springer-Verlag, Berlin, Heidelberg, and New York, 1980. Zbl0452.06001MR0614752
  3. Martinez J., Unique factorization in partially ordered sets, Proc. Amer. Math. Soc. 33 (1972), 213-220. (1972) Zbl0241.06007MR0292723
  4. Novak D., Generalization of continuous posets, Trans. Amer. Math. Soc. 272 (1982), 645-667. (1982) Zbl0504.06003MR0662058
  5. Raney G., A subdirect-union representation for completely distributive lattices, Proc. Amer. Math. Soc. 4 (1953), 518-522. (1953) MR0058568
  6. Venugopalan P., Z -continuous posets, Houston J. Math. 12 (1986), 275-294. (1986) Zbl0614.06007MR0862043
  7. Venugopalan P., Union complete subset system, Houston J. Math. 14 (1988), 583-600. (1988) MR0998459
  8. Wright J.B., Wagner E.G., Thatcher J.W., A uniform approach to inductive posets and inductive closure, Theor. Computer Science 7 (1978), 57-77. (1978) Zbl0732.06001MR0480224

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.