| Title:
|
A note on topology of $Z$-continuous posets (English) |
| Author:
|
Menon, Venu G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
821-824 |
| . |
| Category:
|
math |
| . |
| Summary:
|
$Z$-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. (English) |
| Keyword:
|
$Z$-continuous posets |
| Keyword:
|
intrinsic topology |
| MSC:
|
06B30 |
| MSC:
|
06B35 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 0888.06005 |
| idMR:
|
MR1440713 |
| . |
| Date available:
|
2009-01-08T18:28:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118890 |
| . |
| Reference:
|
[BE] Bandelt H.J., Erné M.: The category of $Z$-continuous posets.J. Pure Appl. Algebra 30 (1983), 219-226. MR 0724033 |
| Reference:
|
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| Reference:
|
[M] Martinez J.: Unique factorization in partially ordered sets.Proc. Amer. Math. Soc. 33 (1972), 213-220. Zbl 0241.06007, MR 0292723 |
| Reference:
|
[N] Novak D.: Generalization of continuous posets.Trans. Amer. Math. Soc. 272 (1982), 645-667. Zbl 0504.06003, MR 0662058 |
| Reference:
|
[R] Raney G.: A subdirect-union representation for completely distributive lattices.Proc. Amer. Math. Soc. 4 (1953), 518-522. MR 0058568 |
| Reference:
|
[V1] Venugopalan P.: $Z$-continuous posets.Houston J. Math. 12 (1986), 275-294. Zbl 0614.06007, MR 0862043 |
| Reference:
|
[V2] Venugopalan P.: Union complete subset system.Houston J. Math. 14 (1988), 583-600. MR 0998459 |
| Reference:
|
[WWT] 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. Zbl 0732.06001, MR 0480224 |
| . |
