Resumen de Zero-dimensional Closed Set Aposyndesis and Hyperspaces

Jorge M. Martínez-Montejano

• A continuum is a compact metric space. It is said that a continuum X is zero-dimensional closed set aposyndetic provided that for each zero-dimensional closed subset A of X and for each p in X minus A, there exists a subcontinuum M of X such that p is in the interior of M and M does not intersect A. It is shown that if X is a continuum and n is a natural number, then both the hyperspace of nonempty closed subsets of X and the n-fold hyperspace of X are zero-dimensional closed set aposyndetic