Connectedness im kleinen and components in $C(X)$

Joo Ran Moon; Kul Hur; Choon Jai Rhee

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

QR
Code

Article

HOME

ALL ARTICLES

View

Bull. Korean Math. Soc. 1997; 34(2): 225-231

Printed June 1, 1997

Connectedness im kleinen and components in $C(X)$

Joo Ran Moon, Kul Hur, and Choon Jai Rhee

Wonkwang University, Wonkwang University, Wayne State University

Abstract

Go to

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