Aposyndesis in strictly non-mutually-aposyndetic, plane continua
by
Eldon Vought
California State University,Chico
Coauthors: E. E. Grace

We prove that if M is a strictly non-mutually-aposyndetic, plane continuum, i.e.,a plane continuum in which every two subcontinua with nonvoid interiors intersect, then M is aposyndetic at no more than one point. This strengthens a result given at the 2002 Chico Topology Conference. With the aid of a weak-cutpoint theorem of F. B. Jones, this yields a new proof, of the conjecture of Howard Cook, that any plane continuum, in which every two subcontinua with nonvoid interior intersect, has a weak cutpoint.

Date received: February 26, 2003