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Lightness of Induced Maps and Homeomorphisms

Published online by Cambridge University Press:  20 November 2018

Javier Camargo
Javier Camargo*
Affiliation:
Escuela de Matemáticas, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga, Santander, A.A. 678, Colombiae-mail: jecamar@uis.edu.co
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Abstract

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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

54B2054E40light mapsinduced mapscontinuahyperspaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 4 , 01 December 2011 , pp. 607 - 618
Copyright
Copyright © Canadian Mathematical Society 2011

References

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