It is shown that there is no Whitney map on the hyperspace for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).
@article{bwmeta1.element.bwnjournal-article-cmv83i2p305bwm, author = {Janusz Charatonik and W\l odzimierz Charatonik}, title = {Whitney maps-a non-metric case}, journal = {Colloquium Mathematicae}, volume = {84/85}, year = {2000}, pages = {305-307}, zbl = {0953.54013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv83i2p305bwm} }
Charatonik, Janusz; Charatonik, Włodzimierz. Whitney maps-a non-metric case. Colloquium Mathematicae, Tome 84/85 (2000) pp. 305-307. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv83i2p305bwm/
[000] [1] R. Engelking, General Topology, Heldermann, Berlin, 1989.
[001] [2] A. Gutek, A generalization of solenoids, in: Topology (Budapest, 1978), Colloq. Math. Soc. János Bolyai 23, North-Holland, Amsterdam, 1980, 547-554.
[002] [3] A. Gutek and C. L. Hagopian, A nonmetric indecomposable homogeneous continuum every proper subcontinuum of which is an arc, Proc. Amer. Math. Soc. 86 (1982), 169-172. | Zbl 0489.54031
[003] [4] A. Illanes and S. B. Nadler, Jr., Hyperspaces, Dekker, New York, 1999.
[004] [5] S. B. Nadler, Jr., Hyperspaces of Sets, Dekker, New York, 1978.