Abstract
If P and X are ordered sets with the fixed point property, does P×X have the fixed point property? In case one of P and X is finite the answer is yes. Here we answer the question affirmatively when P has width at most three.
Similar content being viewed by others
References
Duffus, D. and Sauer, N.: Fixed points of products and the fixed point property, Order 4 (1987), 221–231.
Duffus, D., Rival, I. and Simonovits, M.: Spanning retracts of a partially ordered set, Discrete Math. 32 (1980), 1–7.
Farley, J. D.: The fixed point property for posets of small width, Order 14 (1997), 125–143.
Farley, J. D.: Perfect sequences of chain-complete posets, Discrete Math. 167 (1997), 271–298.
Li, B. and Milner, E. C.: A chain complete poset with no infinite antichain has a finite core, Order 10(1993), 55–63.
Li, B. and Milner, E. C.: From finite posets to chain complete posets having no infinite antichain, Order 12 (1995), 159–171.
Rival, I.: Unsolved problems, Order 1 (1984), 103–105.
Roddy, M. S.: Cores and retracts, Order 11 (1994), 1–10.
Roddy, M. S.: Fixed points and products, Order 11 (1994), 11–14.
Roddy, M. S., Rutkowski, A. and Schröder, B. S.: Fixed points and products: A more general version, Unpublished manuscript (1994).
Rutkowski, A.: Multifunctions and the fixed point property for products of ordered sets, Order 2 (1985), 257–267.
Rutkowski, A.: The fixed point property for sums of posets, Demonstratio Math. 4 (1986), 1077–1088.
Rutkowski, A. and Schröder, B. S.: Retractability and the fixed point property, Order 4 (1994), 353–359.
Schröder, B. S.: The fixed point property for 11-element sets, Order 10 (1993), 329–347.
Schröder, B. S.: Uniqueness of the core for chain-complete ordered sets, Order 17 (2000), 207–214.
Tran, T.: NSERC undergraduate summer research report, Brandon University, 1997.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roddy, M.S. Fixed Points and Products: Width 3. Order 19, 319–326 (2002). https://doi.org/10.1023/A:1022883828701
Issue Date:
DOI: https://doi.org/10.1023/A:1022883828701