Mutual aposyndesis in symmetric products
by
Jorge M. Martinez-Montejano
West Virginia University

A continuum is a compact connected metric space. Mutual aposyndesis is the continuum theory analogue of the Hausdorff separation property; namely, a continuum X is said to be mutually aposyndetic provided that for each two different points x, y in X there exist disjoint subcontinua K and L of X such that x in intK and y in intL. The n-fold symmetric product of a continuum X is {A subset X: A =/= \emptyset and A has at most n points} with the Vietoris topology; it is denoted by F_n(X). It is proved that F_n(X) is mutually aposyndetic for n >= 3 (the resul for n=2 is false).

Date received: June 22, 1999