Zero-dimensional closed set aposyndesis and hyperspaces
by
Jorge M. Martínez-Montejano
Instituto de Matemáticas, UNAM

We say that a continuum is zero-dimensional closed set aposyndetic provided that for each zero-dimensional closed subset A of X and for each p Î X-A, there exist a subcontinuum M of X such that p Î intM and MÇA=Æ. We show that if X is a continuum and n is a natural number, then both 2^X, the hyperspace of nonempty closed subsets of X, and C_n(X), the n-fold hyperspace of X, are zero-dimensional closed set aposyndetic.

This answers a question by E. K. Van Douwen and Jack T. Goodykoontz, Jr.

Date received: February 28, 2005