An update on the elusive fixed-point property
by
Charles L. Hagopian
California State University, Sacramento

R. H. Bing's 1969 Monthly article, "The elusive fixed point property," has been an invaluable guide to generations of mathematicians. Bing was interested in the fundamental problem of determining which continua have the fixed-point property. His article consists of twelve questions and a variety of related theorems and examples. We review Bing's questions, some results that followed the publication of his article, and some related unsolved problems. Although considerable progress has been made in this area of fixed-point theory, several general problems remain unsolved. It is still unknown whether every plane continuum that does not separate the plane has the fixed-point property.

Date received: January 31, 2006