ALMOST MESHED LOCALLY CONNECTED CONTINUA WITHOUT UNIQUE n-FOLD HYPERSPACE SUSPENSION

摘要

For a metric continuum X and n is an element of N, we consider the hyperspaces C-n(X) (respectively, F-n(X)) of all nonempty closed subsets of X with at most n components (respectively, n points). Let HSn(X) be the quotient space C-n(X)/F-n(X) with the quotient topology. In this paper we prove that: (1) if X and Y are almost meshed locally connected continua and HSn(X) is homeomorphic to HSn(Y), then X is homeomorphic to Y, for each n is an element of N - {1, 2}; (2) there are almost meshed locally connected continua without unique n-fold hyperspace suspension, for each n is an element of N.