Fixed point theorems for acyclic and dendritic spaces

Thomas Bourque Muenzenberger and Raymond Earl Smithson

Vol. 72 (1977), No. 2, 501–512

DOI: 10.2140/pjm.1977.72.501

Abstract

A mod is a partially ordered set (X,≦) such that: (i) x ∧ y exists for all x,y ∈ X. (ii) L(x) is totally ordered for all x ∈ X. (iii) (X,≦) is conditionally complete and order dense. Fixed point theorems for certain functions on totally ordered mods are extended to multifunctions on arbitrary mods by using weak continuity conditions. Characterizations of continuity are also given for certain functions on mods. Mods are shown to be algebraic models for acyclic and dendritic spaces.

Mathematical Subject Classification 2000

Primary: 54H25

Milestones

Received: 2 February 1977

Published: 1 October 1977