The Journal of the Indian Mathematical Society

Chain-Completeness and Fixed Points in Partially Ordered Sets


Affiliations

  • Government College, Department of Mathematics, 671 123, India
  • University of Mangalore, Department of Mathematics, Mangalore, 574 199, India

Abstract

In this paper different characterizations of chain-complete posets are given in terms of the fixed points of certain class of functions. Further, an error in the proof of a result of Taskovic is pointed out and a correct proof of the same is given.

Keywords

Poset, Chain-Completeness, Fixed Point Property.

Subject Discipline

Mathematical Sciences

Full Text:

References

S. Abian and A. Brown, A theorem on partially ordered sets with applications to fixed point theorems, Canad. J. Math. 13, (1961), 78–82 .

P. Crawley and R. P. Dilworth, Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs, NJ, (1973).

A. C. Davis, A characterization of complete lattices, Pacific J. Math. 5, (1955), 311–319.

Josef Niederle, A useful fixpoint theorem, Rendiconti del Circolo Matematico di Palermo, Serie II, Tomo XLVII, (1998), 463–464.

J. Klime's, Fixed edge theorems for complete lattices, Arch. Math. 17, (1981), 227–234.

G. Markowsky, Chain-complete posets and directed sets with applications, Algebra Universalis 6, (1976), 53–68.

P. V. R. Murty and V. V. R. Rao, Fixed point theorems on chain complete partially ordered sets, Southeast Asian Bulletin of Mathematics 25, (2002), 705–710.

A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math. 5, (1955), 285–309.

M. R. Taskovic, Characterizations of inductive posets with applications, Proc. Amer. Math. Soc. 104, (1988), 650–659.


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