Geodesic
Induced near-homeomorphisms
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 1, pp. 133-137.

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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.
Classification : 54B20, 54E40
Keywords: cell-like; continuum; dendrite; hyperspace; induced mapping; monotone; \newline near-homeomorphism; refinable 
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Charatonik, Włodzimierz J. Induced near-homeomorphisms. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 1, pp. 133-137. http://geodesic.mathdoc.fr/item/CMUC_2000__41_1_a11/