On Convergence of Sequences in Complete Lattices

Wojciech Olszewski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We generalize the famous Tarski result by showing that: if X is a complete lattice, and f : X → X is an order-preserving mapping, then for all points x ∈ X, the limit superior and the limit inferior of the (possibly transfinite) sequence of iterations x, f(x), f2(x).., fβ(x),.. are fixed points of f. These limits are the sharp fixed-point bounds between which sufficiently large transfinite iterations are located.

Original languageEnglish (US)
Pages (from-to)251-255
Number of pages5
Issue number2
StatePublished - Jul 2021


  • Tarski fixed-point theorem

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics


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