We construct examples of mappings $f$ and $g$ between locally connected continua such that $2^f$ and $C(f)$ are near-homeomorphisms while $f$ is not, and $2^g$ is a near-homeomorphism, while $g$ and $C(g)$ are not. Similar examples for refinable mappings are constructed.
@article{119147, author = {W\l odzimierz J. Charatonik}, title = {Induced near-homeomorphisms}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {41}, year = {2000}, pages = {133-137}, zbl = {1038.54005}, mrnumber = {1756933}, language = {en}, url = {http://dml.mathdoc.fr/item/119147} }
Charatonik, Włodzimierz J. Induced near-homeomorphisms. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 133-137. http://gdmltest.u-ga.fr/item/119147/
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