Decomposable chainable continua
J. B. Fugate · Transactions of the American Mathematical Society · 1966
In this paper, we supply some answers to the following question.What are sufficient conditions that a compact continuum be chainable?It is well known that chainable compact metric continua must be both a-triodic and hereditarily unicoherent.If M is a compact metric continuum which is a-triodic and hereditarily unicoherent, we show in Theorem 1 that M is chainable if it is the union of two continua, each of which is chainable.Conditions which imply chainability are of interest because of their possible application to the homogeneity problem, i.e., the problem of characterizing the homogeneous bounded plane continua.Bing [4] has shown that the only homogeneous chainable plane continuum is the pseudo-arc.The author wishes to express his appreciation to Professor Steve Armentrout, not only for suggesting these problems, but also for his aid and encouragement throughout the author's graduate studies.