JP Journal of Geometry and Topology
Volume 4, Issue 1, Pages 13 - 21
(March 2004)
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ARC-SMOOTH
CONTINUUM X ADMITS A
WHITNEY MAP FOR
C(X)
IFF IT IS METRIZABLE
Ivan Loncar (Croatia)
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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 particular, locally connected or rim-metrizable
continuum admits a Whitney map if and only if it
is metrizable. In this paper we will show that
an arc-smooth continuum X admits a
Whitney map for C(X)
if and only if it is metrizable. |
| Keywords and phrases: arc-smooth continuum, arboroid, hyperspace, inverse system, Whitney map. |
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