Subcontinua with degenerate tranches in hereditarily decomposable continua

Academic Article


  • A hereditarily decomposable, irreducible, metric continuum M admits a mapping f onto [0, 1] such that each is a nowhere dense subcontinuum. The sets f-1(t) are the tranches of M and f-1(t) is a tranche of cohesion if (FORMAL PRESENTED). The following answer a question of Mahavier and of E. S. Thomas, Jr. Theorem. Every hereditarily decomposable continuum contains a subcontinuum with a degenerate tranche. Corollary. If in an irreducible hereditarily decomposable continuum each tranche is nondegenerate then some tranche is not a tranche of cohesion. The theorem answers a question of Nadler concerning arcwise accessibility in hyperspaces. © 1983 American Mathematical Society.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Oversteegen LG; Tymchatyn ED
  • Start Page

  • 717
  • End Page

  • 724
  • Volume

  • 278
  • Issue

  • 2