Subcontinua with degenerate tranches in hereditarily decomposable continua

Lex G. Oversteegen, E. D. Tymchatyn
1983 Transactions of the American Mathematical Society  
A hereditarily decomposable, irreducible, metric continuum M admits a mapping/onto [0,1] such that each/"'(f) is a nowhere dense subcontinuum. The sets/~'(r) are the tranches of M and/"' . 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
more » ... sion. The theorem answers a question of Nadler concerning arcwise accessibility in hyperspaces.
doi:10.1090/s0002-9947-1983-0701520-7 fatcat:dllzzpoqgzbh7lpvokkys3742a