Publications de l'Institut Mathematique 2003 Volume 73, Issue 87, Pages: 97-113
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Non-metric Rim-metrizable continua and unique hyperspace
A class Λ of continua is said to be C-determined provided that if X, Y _ Λ and C(X) ≈ C(Y), then X ≈ Y. A continuum X has unique hyperspace provided that if Y is a continuum and C(X) ≈ C(Y), then X ≈ Y. In the realm of metric continua the following classes of continua are known to have unique hyperspace: hereditarily indecomposable continua, smooth fans (in the class of fans) and indecomposable continua whose proper and non-degenerate subcontinua are arcs. We prove that these classes have unique hyperspace in the realm of rim-metrizable non-metric continua. .
Keywords: hyperspace, continuum, inverse system
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