PUBLICATIONS DE L'INSTITUT MATH\'EMATIQUE (BEOGRAD) (N.S.) EMIS ELibM Electronic Journals Publications de l'Institut Mathématique (Beograd)
Vol. 73(87), pp. 97-113 (2003)

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Ivan Lon\v car

Faculty of Organizations and Informatics, Varazdin, Croatia

Abstract: 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.

Keywords: hyperspace; continuum; inverse system

Classification (MSC2000): 54B20; 54B35

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Electronic version published on: 1 Jan 1970. This page was last modified: 14 Apr 2004.

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