Geodesic
Non-metric Rim-metrizable Continua and Unique Hyperspace
Publications de l'Institut Mathématique, _N_S_73 (2003) no. 87, p. 97 .

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A class $\Lambda$ of continua is said to be $C$\textit{-determined} provided that if $X,Y\in\Lambda$ and $C(X)\approx C(Y)$, then $X\approx Y$. A continuum $X$ has \textit{unique hyperspace} provided that if $Y$ is a continuum and $C(X)\approx C(Y)$, then $X\approx Y$. 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.
DOI : 10.2298/PIM0373097L
Classification : 54B20 54B35
Keywords: hyperspace, continuum, inverse system 
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     author = {Ivan Lon\v{c}ar},
     title = {Non-metric {Rim-metrizable} {Continua} and {Unique} {Hyperspace}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {97 },
     publisher = {mathdoc},
     volume = {_N_S_73},
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Ivan Lončar. Non-metric Rim-metrizable Continua and Unique Hyperspace. Publications de l'Institut Mathématique, _N_S_73 (2003) no. 87, p. 97 . doi : 10.2298/PIM0373097L. http://geodesic.mathdoc.fr/articles/10.2298/PIM0373097L/

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