A characterisation of the absolute quasi-retracts in a class of acyclic continua

Author:

Akis V.N.,Curtis D.W.

Abstract

The class of quasi-retracts of AR's (AQR's) was first considered by Stallings, who observed that every AQR has the fixed point property. More recently, it has been shown that the class of AQR's is closed with respect to the operations of taking cones, suspensions, or products with AR's, and that no AQR separates a Euclidean space. In this paper we show that every AQR is acyclic, and we obtain a simple, direct characterization of the AQR's in a certain class of acyclic continua.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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1. An update on the elusive fixed-point property;Open Problems in Topology II;2007

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