We show that there exists a C*-smooth continuum X such that for every continuum Y the induced map C(f) is not open, where f: X × Y → X is the projection. This answers a question of Charatonik (2000).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-6, author = {W\l odzimierz J. Charatonik and Alejandro Illanes and Ver\'onica Mart\'\i nez-de-la-Vega}, title = {Induced open projections and C*-smoothness}, journal = {Colloquium Mathematicae}, volume = {131}, year = {2013}, pages = {73-94}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-6} }
Włodzimierz J. Charatonik; Alejandro Illanes; Verónica Martínez-de-la-Vega. Induced open projections and C*-smoothness. Colloquium Mathematicae, Tome 131 (2013) pp. 73-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-6/