The fixed-point property for deformations of uniquely arcwise connected continua
A mapping f of a space M into M is called a deformation of M if there exists a mapping h of \(M\times [0,1]\) onto M such that \(h(x,0)=x\) and \(h(x,1)=f(x)\) for each point x of M. The author proves that if M is a uniquely arcwise connected metric continuum, then every deformation of M has a fixed point. Some related results and problems are discussed.
scientific article; zbMATH DE number 3980003
scientific article