Chainable continua without almost unique hyperspace
by
Gerardo Acosta
Universidad Nacional Autónoma de México
Coauthors: Janusz J. Charatonik (University of Wroclaw), Alejandro Illanes (Universidad Nacional Autónoma de México)

For a given continuum X let C(X) denotes the hyperspace of subcontinua of X and consider a family F(X) of continua Y such that: (1) no to distinct members of F(X) are homeomorphic, (2) C(Y) is homeomorphic to C(X) for each member Y of F(X), and (3) if Z is a continuum such that C(Z) is homeomorphic to C(X), then Z is homeomorphic to Y for some member Y of F(X). We said that a continuum X has unique hyperspace provided that F(X) = X. If F(X) is finite and consists of more that one element we said that X has almost unique hyperspace. A. Illanes has asked if there are chainable continua X for which the family F(X) consists of at least five elements which are chainable too. In this talk we preset a positive answer to the above question by showing that there are chainable continua X for which the family F(X) contains infinitely many chainable continua.

Date received: February 2, 2000