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# Lightness of Induced Maps and Homeomorphisms

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Published:2011-03-10
Printed: Dec 2011
• Javier Camargo,
Escuela de Matemáticas, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga, Santander, A.A. 678, Colombia
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## Abstract

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 $C(C(f))$.
 Keywords: light maps, induced maps, continua, hyperspaces
 MSC Classifications: 54B20 - Hyperspaces 54E40 - Special maps on metric spaces

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