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Lightness of Induced Maps and Homeomorphisms |
Canad. Math. Bull. 54(2011), 607-618
Published:2011-03-10
Printed: Dec 2011
Printed: Dec 2011
- Javier Camargo,
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 |