On Convergence of Sequences in Complete Lattices

Wojciech Olszewski

doi:10.1007/s11083-020-09538-z

On Convergence of Sequences in Complete Lattices

Wojciech Olszewski^*

^*Corresponding author for this work

Economics

Research output: Contribution to journal › Article › peer-review

Abstract

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).., f^β(x),.. are fixed points of f. These limits are the sharp fixed-point bounds between which sufficiently large transfinite iterations are located.

Original language	English (US)
Pages (from-to)	251-255
Number of pages	5
Journal	Order
Volume	38
Issue number	2
DOIs	https://doi.org/10.1007/s11083-020-09538-z
State	Published - Jul 2021

Keywords

Tarski fixed-point theorem

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Computational Theory and Mathematics

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On Convergence of Sequences in Complete Lattices

Abstract

Keywords

ASJC Scopus subject areas

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