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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:
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


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