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NON-METRIC RIM-METRIZABLE CONTINUA
AND UNIQUE HYPERSPACE
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 Full text of the article:
Electronic version published on: 1 Jan 1970.
This page was last modified: 14 Apr 2004.
© 1970 Mathematical Institute of the Serbian Academy of Science and Arts
© 1970--2004 ELibM and FIZ Karlsruhe / Zentralblatt MATH for
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Publications de l'Institut Mathématique (Beograd)