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Lightness of Induced Maps and Homeomorphisms
Published online by Cambridge University Press: 20 November 2018
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 $C(C(f))$.
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- Copyright © Canadian Mathematical Society 2011
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