Connectedness im kleinen and components in $C(X)$
Bull. Korean Math. Soc. 1997 Vol. 34, No. 2, 225-231
Joo Ran Moon, Kul Hur, and Choon Jai Rhee
Wonkwang University, Wonkwang University, Wayne State University
Abstract : If the hyperspace $ C(X) $ is connected im kleinen at $ A \in \Cal A(a) $, is the admissible fiber at $ a $,then $ C(X) $ is connected im kleinen at each subcontinuum $ B $ which contains $ A $. In case $ X $ has property $ k $ and $ C(X) $ is not connected im kleinen at a point $ A \in C(X)$, $ C(X) $ is not connected im kleinen at each subcontinuum of $ A $.
Keywords : hyperspace, connected im kleinen, metric continuum, admissible
MSC numbers : 54B20
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