| Title:
|
Weak chain-completeness and fixed point property for pseudo-ordered sets (English) |
| Author:
|
Bhatta, S. Parameshwara |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
365-369 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point. (English) |
| Keyword:
|
pseudo-ordered set |
| Keyword:
|
trellis |
| Keyword:
|
complete trellis |
| Keyword:
|
fixed point property |
| Keyword:
|
weak chain completeness |
| MSC:
|
06B05 |
| idZBL:
|
Zbl 1081.06004 |
| idMR:
|
MR2137143 |
| . |
| Date available:
|
2009-09-24T11:23:32Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127983 |
| . |
| Reference:
|
[1] P. Crawley and R. P. Dilworth: Algebraic Theory of Lattices.Prentice-Hall, Englewood Cliffs, 1973. |
| Reference:
|
[2] J. Lewin: A simple proof of Zorn’s lemma.Amer. Math. Monthly 98 (1991), 353–354. Zbl 0749.04002, MR 1103192, 10.2307/2323807 |
| Reference:
|
[3] G. Markowski: Chain-complete posets and directed sets with applications.Algebra Universalis 6 (1976), 54–69. MR 0398913 |
| Reference:
|
[4] H. L. Skala: Trellis theory.Algebra Universalis 1 (1971), 218–233. Zbl 0242.06003, MR 0302523, 10.1007/BF02944982 |
| Reference:
|
[5] H. Skala: Trellis Theory.Mem. Amer. Math. Soc. 121, Providence, 1972. Zbl 0242.06004, MR 0325474 |
| . |
