Geodesic
Lightness of Induced Maps and Homeomorphisms
Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 607-618

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DOI

An example is given of a map $f$ defined between arcwise connected continua such that $C(f)$ is light and ${{2}^{f}}$ is not light, giving a negative answer to a question of Charatonik and Charatonik. Furthermore, given a positive integer $n$ , we study when the lightness of the induced map ${{2}^{f}}$ or ${{C}_{n}}(f)$ implies that $f$ is a homeomorphism. Finally, we show a result in relation with the lightness of $C(C(f))$ .
DOI : 10.4153/CMB-2011-040-9
Mots-clés : 54B20, 54E40, light maps, induced maps, continua, hyperspaces 
Camargo, Javier. Lightness of Induced Maps and Homeomorphisms. Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 607-618. doi: 10.4153/CMB-2011-040-9
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     author = {Camargo, Javier},
     title = {Lightness of {Induced} {Maps} and {Homeomorphisms}},
     journal = {Canadian mathematical bulletin},
     pages = {607--618},
     year = {2011},
     volume = {54},
     number = {4},
     doi = {10.4153/CMB-2011-040-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-040-9/}
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