Javier Camargo

Lightness of Induced Maps and Homeomorphisms

An example is given of a map f defined between arcwise connected continua such thatC( 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 Cn( f ) implies that f is a homeomorphism. Finally, we show a result in relation with the lightness ofC(C( f )). Escuela de Matematicas, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga, Santander, A.A. 678, Colombia e-mail: jecamar@uis.edu.co Received by the editors November 5, 2008. Published electronically March 10, 2011. The research in this paper is part of the author’s Ph.D. Dissertation at the Universidad Nacional Autonoma de Mexico, under the supervision of Dr. Sergio Macias. AMS subject classification: 54B20, 54E40.