Isotone relations and the fixed point property for posets

DOI10.1016/0012-365X(84)90188-2zbMath0546.06003OpenAlexW2020382964MaRDI QIDQ798340

James W. Walker

Publication date: 1984

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(84)90188-2

zbMATH Keywords

relationsisotone mappingsdismantlablefinite ordered setisotone relationorder homotopy equivalentrelational fixed point property

Mathematics Subject Classification ID

Partial orders, general (06A06) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items (25)

Dismantlable graphs and posets, fixed clique property ⋮ Cores and retracts ⋮ Perfect sequences of chain-complete posets ⋮ Fixed points of products and the strong fixed point property ⋮ From finite posets to chain complete posets having no infinite antichain ⋮ Lazy Relations ⋮ Interval-dismantling for lattices ⋮ Preservation of the coincidence point existence property under some discrete transformations of a pair of mappings of metric spaces ⋮ Fixed points of mappings on ordered sets ⋮ Preservation of the existence of fixed and coincidence points under homotopy of mappings of ordered sets ⋮ Foldings in graphs and relations with simplicial complexes and posets ⋮ On preservation of common fixed points and coincidences under a homotopy of mapping families of ordered sets ⋮ The strong fixed point property for lexicographic sums ⋮ Fixed point property and formal concept analysis ⋮ A Digital Version of the Kakutani Fixed Point Theorem for Convex-valued Multifunctions ⋮ Isotone relations revisited ⋮ Multivalued homotopy on an ordered set, fixed and coincidence points of mappings, and applications in game theory ⋮ Power structures ⋮ A Lefschetz fixed point theorem for multivalued maps of finite spaces ⋮ Fixed point theorems for ordered sets \(P\) with \(P\setminus \{a, c\}\) as retract ⋮ Automorphisms and products of ordered sets ⋮ A fixed point theorem for multifunctions and an application ⋮ Algorithms for the fixed point property ⋮ The uniqueness of the core ⋮ Multifunctions and the fixed point property for products of ordered sets

Cites Work

• Unnamed Item
• A structure theory for ordered sets
• A fixed point theorem for finite partially orderes sets
• Galois connections and the Leray spectral sequence
• A Theorem on Partially Ordered Sets, With Applications to Fixed Point Theorems
• Retracts and the Fixed Point Problem for Finite Partially Ordered Sets
• Finite Topological Spaces
• Fixed Points of Order Preserving Multifunctions
• Fixed points in partially ordered sets

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