Resumen de Ordered embeddings of symmetric products

Gloria Andablo-Reyes, Víctor Neumann Lara

• Let X and Y be metric continua. Let Fn(X) (resp., Fn(Y)) be the hyperspace of nonempty closed subsets of X (resp., Y) which contain at most n elements. We say that the hyperspace Fn(X) can be orderly embedded in Fm(Y) provided that there exists an embedding h from Fn(X) to Fm(Y) such that if A,B are elements of Fn(X) and A is contained in B, then h(A) is contained in h(B). In this paper we prove:

  (a) If n is minor or equal than m, m is minor than 2n and Fn(X) can be orderly embedded in Fm(Y), then X can be embedded in Y.

  (b) There exist continua X and Y such that, for each n greater than 1, Fn(X) can be orderly embedded in F2n(Y) and X can not be embedded in Y