Glasnik Matematicki, Vol. 38, No.2 (2003), 395-411.
A FAN X ADMITS A WHITNEY MAP FOR
C(X) IFF IT IS METRIZABLE
Ivan Loncar
Faculty of Organization and Informatics Varazdin, University of Zagreb,
Pavlinska 2, 42000 Varazdin, Croatia
e-mail: ivan.loncar1@vz.tel.hr
Abstract. Let X be a non-metric continuum, and
C(X) be the hyperspace of
subcontinua
of X. It is known that there is no Whitney map on the hyperspace
2X for non-metrizable Hausdorff compact spaces
X. On the other
hand, there exist non-metrizable continua which admit and ones
which do not admit a Whitney map for C(X).
In this paper we will
show that a generalized fan X admits a Whitney map for
C(X) if and only if it is metrizable.
2000 Mathematics Subject Classification.
54F15, 54B20, 54B35.
Key words and phrases. Fan, hyperspace, inverse system, Whitney map.
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