Continua in R∗

AbstractR∗ is the Stone–Čech remainder of the real line. We prove that every decomposable continuum in R∗ is a section of a standard continuum. Every indecomposable continuum in R∗ is the union of a family of standard continua. About the general structures of continua in R∗, the following statements are true: 1.(1) Let C and D be continua in R∗. If one of them is indecomposable, then C ⊂ D, D ⊂ C or C ∩ D = Ø. 1.(2) R∗ is hereditarily unicoherent, i.e., any intersection of continua in R∗ is a continuum. Moreover, any intersection of indecomposable continua in R∗ is indecomposable. 1.(3) The closure of the union of a chain of indecomposable continua in R∗ is an indecomposable continuum. 1.(4) A point x of R∗ is not a sub cutpoint iff {x} is the intersection of a maximal chain of nondegenerate indecomposable continua in R∗. 1.(5) There are no Q-points in ω∗ iff every composant of β[0, ∞)−[0, ∞) is the union of a strictly increasing sequence of proper indecomposable subcontinua. 1.(6) The principal NCF is equivalent to the statement that β[0, ∞)−[0, ∞) is the union of a strictly increasing sequence of proper indecomposable subcontinua.Now we know in ZFC that there are nine different continua in R∗